On (A={1,2,3}), (R={(a,b):a<b}). Is (R) reflexive or not?
Correct answer: B
Step 1: Reflexivity needs ((1,1),(2,2),(3,3)). Step 2: No number satisfies (a<a). Step 3: The relation (<) is not reflexive.
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Reflexive relation
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Easy · Level 8 · less than relation,not reflexive,relations
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- Reflexive
- Not reflexive
- Universal
- Singleton relation
Easy · Level 8 · definition,reflexive relation,set theory
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- ((x,x)\in R)
- ((x,y)\in R) for every (y)
- ((y,x)\in R) for every (y)
- ((x,x)\notin R)
Easy · Level 8 · add missing pair,reflexive relation,easy
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- ((0,1))
- ((1,0))
- ((1,1))
- ((0,0))
Easy · Level 8 · definite pair,reflexive relation,self pair
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- ((p,q))
- ((q,r))
- ((r,r))
- ((r,p))
Easy · Level 8 · identity relation,minimum reflexive relation,mcq
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- Smallest reflexive relation
- Empty relation
- Not reflexive
- Relation with all possible pairs
Easy · Level 8 · checking reflexivity,exam tip,relations
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- Whether all ((a,a)) pairs are present
- Whether all ((a,b)) have (a\ne b)
- Whether the relation has only one pair
- Whether the set is not empty
Easy · Level 8 · reflexive check,ordered pairs,class 12
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- (R) is reflexive
- (R) is not reflexive
- (R) is empty
- (R) has no self-pair
Easy · Level 8 · missing diagonal pair,not reflexive,relations
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- ((1,2))
- ((2,2))
- ((3,1))
- ((1,3))
Easy · Level 8 · relation condition,reflexive relation,equality
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- Because (a-a=0) for every (a)
- Because (a-b=1) always
- Because (a+b=0) always
- Because (a\ne b) is required
Easy · Level 8 · even sum relation,reflexive relation,pyq pattern
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- Yes, because (a+a=2a) is even
- No, because (1+2) is odd
- No, because only equal numbers are needed
- Yes, because all pairs are taken
Easy · Level 8 · odd sum relation,not reflexive,relations
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- Reflexive
- Not reflexive
- Universal
- Identity relation
Easy · Level 8 · divisibility relation,reflexive relation,easy
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- Yes, because every (a) divides itself
- No, because (2) does not divide (3)
- No, because only (1) divides all
- Yes, because all numbers are equal
Easy · Level 8 · condition based relation,not reflexive,mcq
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- Because (a=a+1) is never true
- Because (1=2+1)
- Because all pairs are present
- Because every number equals itself
Easy · Level 8 · singleton set,reflexive relation,ordered pair
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- (\varnothing)
- ({(10,10)})
- ({(10,1)})
- ({(1,10)})
Easy · Level 8 · number of reflexive relations,counting,relations
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- (1)
- (2)
- (4)
- (8)
Easy · Level 8 · counting reflexive relations,n elements,easy
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- (2^3)
- (2^6)
- (2^9)
- (3^2)
Easy · Level 8 · must contain pair,self pair,reflexive
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- ((1,2))
- ((2,1))
- ((3,3))
- ((1,3))
Easy · Level 8 · sufficient condition,reflexive relation,concept
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- Yes
- No
- Only when no extra pair is present
- Only when (R) is empty
Easy · Level 8 · definition based mcq,reflexive relation,class 12
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- Every element is related to itself
- No element is related to itself
- Only different elements are related
- The relation is always empty
Easy · Level 8 · extra pair,reflexive relation,exam tip
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- The relation remains reflexive
- The relation will not remain reflexive
- The relation becomes empty
- The self-pairs disappear
A relation (R) on a set (A) is reflexive. What must be true for every (x\in A)?
Correct answer: A
Step 1: The key idea of a reflexive relation is being related to itself. Step 2: This means ((x,x)\in R) for every (x). Step 3: Remembering the definition helps solve such questions quickly.
View question detailsOn (A={0,1}), (R={(0,0),(0,1),(1,0)}). Which pair should be added to make (R) reflexive?
Correct answer: C
Step 1: For (0) and (1), the pairs ((0,0)) and ((1,1)) are required. Step 2: ((0,0)) is already present, but ((1,1)) is missing. Step 3: Add the missing diagonal pair.
View question detailsIf (R) is reflexive on (A={p,q,r}), which pair is definitely in (R)?
Correct answer: C
Step 1: In a reflexive relation, every element is related to itself. Step 2: Since (r) is in (A), ((r,r)) must be present. Step 3: Pairs with different elements are not compulsory.
View question detailsOn (A={1,2,3}), what can (R={(1,1),(2,2),(3,3)}) be called?
Correct answer: A
Step 1: It contains the self-pair of every element. Step 2: It has no extra pairs, so it is the smallest reflexive relation. Step 3: This is also the identity relation on the set.
View question detailsWhat should be checked first while testing whether a relation is reflexive?
Correct answer: A
Step 1: Reflexivity is checked through self-pairs. Step 2: For every element (a), ((a,a)) must be present. Step 3: In exams, list the diagonal pairs directly.
View question detailsOn (A={1,2,3}), (R={(1,1),(2,2),(3,2),(1,3),(3,3)}). Choose the correct statement.
Correct answer: A
Step 1: The required pairs for (A) are ((1,1),(2,2),(3,3)). Step 2: All three are present in (R). Step 3: Other pairs do not affect reflexivity.
View question detailsOn (A={1,2,3}), (R={(1,1),(2,3),(3,3)}). Which missing pair makes (R) not reflexive?
Correct answer: B
Step 1: The elements (1,2,3) need their self-pairs. Step 2: ((1,1)) and ((3,3)) are present, but ((2,2)) is missing. Step 3: Focus on the missing self-pair.
View question detailsThe relation (R={(a,b):a-b=0}) is given on a set of numbers. Why is it reflexive?
Correct answer: A
Step 1: For reflexivity, test an element with itself. Step 2: For every (a), (a-a=0), so ((a,a)\in R). Step 3: Put (b=a) in the condition to check quickly.
View question detailsOn (A={1,2,3,4}), (R={(a,b):a+b\text{ is even}}). Is (R) reflexive?
Correct answer: A
Step 1: For reflexivity, put ((a,a)) into the condition. Step 2: (a+a=2a) is always even, so every ((a,a)) is included. Step 3: Checking the self-pair condition is the fastest method.
View question detailsOn (A={1,2,3}), (R={(a,b):a+b\text{ is odd}}). Is (R) reflexive or not?
Correct answer: B
Step 1: For ((a,a)), the sum is (a+a=2a). Step 2: (2a) is always even, not odd. Step 3: So no self-pair satisfies the condition.
View question detailsOn (A={1,2,3}), (R={(a,b):a) divides (b}). Is (R) reflexive?
Correct answer: A
Step 1: Reflexivity needs ((a,a)) for every (a). Step 2: Every non-zero number divides itself, so ((a,a)) is included. Step 3: In divisibility questions, remember (a\mid a) first.
View question detailsOn (A={1,2,3}), (R={(a,b):a=b+1}). Why is it not reflexive?
Correct answer: A
Step 1: For reflexivity, putting (b=a) would require (a=a+1). Step 2: This is not true for any number. Step 3: A condition that gives no self-pair is not reflexive.
View question detailsIf (A={10}), which relation on (A) is reflexive?
Correct answer: B
Step 1: The singleton set has only (10). Step 2: Reflexivity requires ((10,10)). Step 3: The definition stays the same even for small sets.
View question detailsHow many reflexive relations can be formed on (A={1,2})?
Correct answer: C
Step 1: (A\times A) has (4) pairs. Step 2: ((1,1)) and ((2,2)) are compulsory, while the remaining (2) pairs are optional. Step 3: Hence the number is (2^2=4).
View question detailsA set (A) has (3) elements. How many reflexive relations are possible on (A)?
Correct answer: B
Step 1: Total pairs are (3^2=9). Step 2: The (3) self-pairs are compulsory, so (9-3=6) pairs are optional. Step 3: Each optional pair has two choices, so (2^6) relations are possible.
View question detailsOn (A={1,2,3}), (R) is reflexive. Which pair must be in (R)?
Correct answer: C
Step 1: In a reflexive relation, each element is related to itself. Step 2: Since (3) is an element of the set, ((3,3)) is compulsory. Step 3: Pairs with other elements are not compulsory.
View question detailsOn (A={1,2,3,4}), (R) contains all ((1,1),(2,2),(3,3),(4,4)). Can (R) be called reflexive from this information alone?
Correct answer: A
Step 1: Reflexivity only requires all self-pairs. Step 2: All four required self-pairs are present. Step 3: Whether extra pairs exist or not, the relation is reflexive.
View question detailsWhich of the following statements is correct for a reflexive relation?
Correct answer: A
Step 1: Reflexive means returning to the same element. Step 2: Therefore every element must be related to itself. Step 3: For definition-based questions, remember this key sentence.
View question detailsOn (A={1,2,3}), (R={(1,1),(2,2),(3,3),(2,1)}). What is the effect of having ((2,1)) in (R)?
Correct answer: A
Step 1: All three self-pairs needed for reflexivity are present. Step 2: ((2,1)) is an extra pair and does not remove reflexivity. Step 3: Do not worry about extra pairs; check the required pairs.
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