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Hard Relations, type of relations, equivalence relations MCQs for JEE

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Hard Relations, type of relations, equivalence relations MCQs train multi-concept problem solving — attempt after mastering easy and medium sets (29+ on Goodmarks).

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Part of Sets, Relations and Functions in JEE Main Mathematics.

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Q1MathsUnit 1: Sets, Relations and Functions
Which of the following is NOT equivalent to p→q?\boldsymbol{p} \rightarrow \boldsymbol{q} ?
Q2MathsUnit 1: Sets, Relations and Functions
Assertion The relation R\boldsymbol{R} given by R={(1,3),(4,2),(2,4),(2,3),(3,1)}\boldsymbol{R}=\{(\mathbf{1}, \mathbf{3}),(\mathbf{4}, \mathbf{2}),(\mathbf{2}, \mathbf{4}),(\mathbf{2}, \mathbf{3}),(\mathbf{3}, \mathbf{1})\} on a set A={1,2,3,4}A=\{1,2,3,4\} is not symmetric. Reason For symmetric relation R=R−1\boldsymbol{R}=\boldsymbol{R}^{-1}
Q3MathsUnit 1: Sets, Relations and Functions
Which of the following statements is the contrapositive of the statement, You win the game if you know the rules but are not overconfident.
Q4MathsUnit 1: Sets, Relations and Functions
The contrapositive statement of statement "If xx is prime number, then xx is odd" is
Q5MathsUnit 1: Sets, Relations and Functions
x2=xyx^{2}=x y is a relation (defined on set RR ) which is
Q6MathsUnit 1: Sets, Relations and Functions
Consider the following two statements: P:P: If 7 is an odd number, then 7 is divisible by 2. Q: If 7 is a prime number, then 7 is an odd number If V1V_{1} is the truth value of the contrapositive of P\mathrm{P} and V2V_{2} is the truth value of contrapositive of Q,Q, then the ordered pair (V1,V2)\left(V_{1}, V_{2}\right) equals:
Q7MathsUnit 1: Sets, Relations and Functions
Which of the following statements is the inverse of "Our pond floods whenever there is a thunderstorm."?
Q8MathsUnit 1: Sets, Relations and Functions
R\mathrm{R} is a relation in A\mathrm{A} and (a,b)∉r,(\mathrm{a}, \mathrm{b}) \notin \mathrm{r}, implies (b, a) ∉R\notin \mathrm{R} then R\mathrm{R} is said to be relation

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