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Class 12 · Mathematics
→If (R) and (S) are symmetric relations, which statement about (R\cap S) is correct?
Class 12 · Mathematics
→On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(2,3),(3,2),(1,3),(3,1)}). How many equivalence classes does (R) have?
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) if and only if (a\equiv b \pmod{2}) and (a\equiv b \pmod{3}). Choose the correct conclusion.
Class 12 · Mathematics
→On real numbers, (aRb) if and only if (a^2-b^2\ge0). Choose the correct statement.
Class 12 · Mathematics
→On (A={1,2,3,4,5}), (aRb) if and only if (a=b) or (a+b=6). How many ordered pairs are in the relation?
Class 12 · Mathematics
→If (A={1,2,3,4}), what is the ratio of the number of symmetric relations to the number of reflexive and symmetric relations?
Class 12 · Mathematics
→On (A={1,2,3,4}), (R=A\times A-{(1,4),(4,1)}). Choose the correct classification.
Class 12 · Mathematics
→On (A={1,2,3,4,5,6}), (aRb) if and only if both (a,b) are divisible by (2) or both (a,b) are divisible by (3). Choose the correct conclusion.
Class 12 · Mathematics
→On integers, (aRb) if and only if (a-b) is divisible by (4). What is the equivalence class of (3)?
Class 12 · Mathematics
→On (A={1,2,3,4,5}), (aRb) if and only if (a+b) is a prime number. Choose the correct classification.
Class 12 · Mathematics
→On non-zero real numbers, (aRb) if and only if (\frac{a}{b}) is rational. Choose the correct conclusion.
Class 12 · Mathematics
→On (A={2,3,4,6}), (aRb) if and only if the greatest common divisor of (a) and (b) is greater than (1). What type of relation is it?
Class 12 · Mathematics
→On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(3,4),(1,3),(2,4),(1,4)}). Choose the correct classification.
Class 12 · Mathematics
→On (A={1,2,3,4}), (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)}). Choose the correct conclusion.
Class 12 · Mathematics
→If (x,y) belongs to the inverse relation R^-1, which statement follows directly about R?
Class 12 · Mathematics
→If (R) is transitive on a set, choose the correct statement about (R^{-1}).
Class 12 · Mathematics
→On (A={1,2,3,4}), (aRb) if and only if (a=b) or both (a) and (b) are less than (3). What are the correct equivalence classes?
Class 12 · Mathematics
→On (A={1,2,3,4}), (aRb) if and only if both (a) and (b) are less than (4). Choose the correct classification.
Class 12 · Mathematics
→If (A={1,2,3,4}), how many relations on (A) do not contain all self-pairs?
Class 12 · Mathematics
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