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Class 11 · Mathematics
→On (A={1,2,3}), the identity relation is (I_A={(1,1),(2,2),(3,3)}). What is the correct nature of (I_A)?
Class 11 · Mathematics
→For (A={1,2,3}), which statement is correct about the empty relation (R=\varnothing)?
Class 11 · Mathematics
→Relation (R) is defined on (A={1,2,3}) by (R=A\times A). Which statement about (R) is correct?
Class 11 · Mathematics
→On (A={1,2,4,8}), (aRb) if and only if (a\mid b). Which statement is correct?
Class 11 · Mathematics
→On (A={2,3,6,12}), (aRb) if and only if (a\mid b). Which is the least element of this poset?
Class 11 · Mathematics
→On (A={1,2,3,4}), (aRb) if and only if (a) is less than or equal to (b). Which is the greatest element in (R)?
Class 11 · Mathematics
→If a relation (R) is both symmetric and antisymmetric, which off-diagonal pairs can occur in (R)?
Class 11 · Mathematics
→On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2)}). Which property is false?
Class 11 · Mathematics
→On (\mathcal{P}(S)), relation (A,R,B) if and only if (A\subseteq B). What type of relation is this?
Class 11 · Mathematics
→On (\mathbb{R}), (aRb) if and only if (a\leq b). Which statement is correct?
Class 11 · Mathematics
→For A = {1,2,3,4}, let R = {(a,b) : a+b=5}. What is the correct statement about R?
Class 11 · Mathematics
→On (A={2,3,4,5,6}), (aRb) if and only if (a+b) is prime. Which property is surely true for (R)?
Class 11 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) if and only if (\gcd(a,b)=1). Choose the correct option about (R).
Class 11 · Mathematics
→On (\mathbb{R}), (aRb) if and only if (|a|=|b|). Which is the equivalence class of (-3)?
Class 11 · Mathematics
→On (\mathbb{R}), (aRb) if and only if (a^2=b^2). Which statement about (R) is correct?
Class 11 · Mathematics
→For (A={1,2,3,4}), relation (R={(a,b):a\equiv b\pmod{2}}). Which partition is formed by (R)?
Class 11 · Mathematics
→On (\mathbb{Z}), (aRb) if and only if (a-b) is divisible by (4). How many equivalence classes are formed by this relation?
Class 11 · Mathematics
→On (\mathbb{Z}), (aRb) if and only if (a\equiv b\pmod{5}). Which is the equivalence class of (7)?
Class 11 · Mathematics
→On the set of real numbers (\mathbb{R}), (aRb) if and only if (a-b\in\mathbb{Z}). What is the nature of (R)?
Class 11 · Mathematics
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