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Class 12 · Mathematics
→If (R) is symmetric and (R^2=R\circ R), which statement about (R^2) is correct?
Class 12 · Mathematics
→If (R={(x,y):x=2y}) is defined on real numbers, (R) is not symmetric. Which counterexample is correct?
Class 12 · Mathematics
→If (R={(x,y):xy>0}) is defined on real numbers, which statement is correct about (R)?
Class 12 · Mathematics
→If a relation on (A={1,2,3,4}) is both symmetric and antisymmetric, how many such relations are possible?
Class 12 · Mathematics
→If (R) is both symmetric and antisymmetric, what is true about the off-diagonal pairs of (R)?
Class 12 · Mathematics
→If (R) is symmetric and transitive and ((a,b)\in R), which pair must definitely belong to (R)?
Class 12 · Mathematics
→If (R) is symmetric and has no diagonal pair, which statement is correct?
Class 12 · Mathematics
→If (R) is symmetric on a set (A), what is true about (R\cap\Delta), where (\Delta={(a,a):a\in A})?
Class 12 · Mathematics
→If (R) and (S) are symmetric, what is true about (R\triangle S), where (R\triangle S=(R-S)\cup(S-R))?
Class 12 · Mathematics
→If (R) is symmetric on (A={1,2,3}) and contains exactly one diagonal pair and exactly two off-diagonal ordered pairs, how many such relations are possible?
Class 12 · Mathematics
→If (R={(a,b):a\equiv 2b \pmod{5}}) is defined on integers, is (R) symmetric?
Class 12 · Mathematics
→If (R={(a,b):a\equiv b \pmod{3}}) is defined on integers, what is true about (R)?
Class 12 · Mathematics
→If (A={1,2,3,4}) and (R) is symmetric with ((1,4)\notin R), which conclusion is definite?
Class 12 · Mathematics
→If (R) is symmetric on (A={1,2,3,4}) and exactly one off-diagonal pair group is selected, how many off-diagonal ordered pairs are in (R)?
Class 12 · Mathematics
→If R is symmetric, which statement about A×A−R is correct?
Class 12 · Mathematics
→If (R) is a symmetric relation and (T) is a relation such that (R\subseteq T\subseteq R\cup R^{-1}), what is true about (T)?
Class 12 · Mathematics
→If a symmetric relation on (A={1,2,3}) has exactly (5) pairs, which value is possible for the number of diagonal pairs?
Class 12 · Mathematics
→A set (A) has (n) elements. Which is the correct formula for the number of symmetric relations on (A)?
Class 12 · Mathematics
→If (R={(a,b):a=b+2}) on integers, (R) is not symmetric. Which is the correct counterexample?
Class 12 · Mathematics
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