List of top Mathematics Questions on Set Theory and Logic asked in NIMCET

Define relation \(\sim\) on set \(\{1,2,\dots,10\}\) by \(a \sim b\) if \(a-2b\) is divisible by \(3\), then:

The number of ordered tuples \((p,q,r)\) in truth table for which the statement \((\neg p \lor q)\Rightarrow r\) is true is:

Let \(R\subset \mathbb N\times \mathbb N\). Which of the following statements is necessarily true?

Number of triplets of sets \((A,B,C)\) with \(A,B,C\subseteq \{1,2,3,\ldots,n\}\) such that \[ (A\cap B)\subseteq C\subseteq (A\cup B) \] is: