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Class 12 · Mathematics
→If two equivalence classes ([a]) and ([b]) of an equivalence relation are distinct, what is true about their intersection?
Class 12 · Mathematics
→On (A={1,2,3,4}), an equivalence relation has the single class ({1,2,3,4}). Which relation is it?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) if (a+b) is divisible by (3). Why is this not an equivalence relation?
Class 12 · Mathematics
→On (A=\mathbb{R}), (xRy) if (x-y\geq 0). Why is this not an equivalence relation?
Class 12 · Mathematics
→On real numbers, (xRy) if (x^3=y^3). What is the correct conclusion about this relation?
Class 12 · Mathematics
→An equivalence relation (R) on a set (A) has classes ({a,b}), ({c}), and ({d,e,f}). How many pairs are in (R)?
Class 12 · Mathematics
→On (A=\mathbb{Z}), (aRb) if (a-b) is divisible by (4). How many distinct equivalence classes does this relation have?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) if (a) and (b) leave the same remainder on division by (3). What is ([2])?
Class 12 · Mathematics
→If an equivalence relation on (A={1,2,3}) contains ((1,2)) and ((2,3)), what is the minimum number of pairs in (R)?
Class 12 · Mathematics
→On (A=\mathbb{R}), (xRy) if (x-y=0). Which relation is this?
Class 12 · Mathematics
→On integers, (aRb) if (|a-b|\leq 2). Why is this not an equivalence relation?
Class 12 · Mathematics
→On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1)}). Is (R) an equivalence relation?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6,7,8,9}), (aRb) if (a\equiv b \pmod{3}). How many ordered pairs are in the relation?
Class 12 · Mathematics
→If (R) is an equivalence relation and ((a,b)\in R), which statement is necessarily true?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) if (\lfloor\frac{a}{2}\rfloor=\lfloor\frac{b}{2}\rfloor). Which are the equivalence classes of (R)?
Class 12 · Mathematics
→On integers, (aRb) if (a+b) is divisible by (2). Which statement is correct?
Class 12 · Mathematics
→On (A=\mathbb{R}), (xRy) if (|x|=|y|). What type of relation is this?
Class 12 · Mathematics
→On (A={-2,-1,0,1,2}), (xRy) if (x^2=y^2). What is the equivalence class of (2)?
Class 12 · Mathematics
→If (f:A\to B) is a function and (aRb) if (f(a)=f(b)), what type of relation is (R)?
Class 12 · Mathematics
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