Embibe Experts Solutions for Chapter: Mathematical Logic, Exercise 1: MHT-CET 2020 (13-Oct Shift 1)

If $p$ and $q$ are true and $r$ and $s$ are false statements, then which of the following is true?

The statement pattern $\left[\left(p\vee q\right)\wedge ~p\right]\wedge \left(~q\right)$ is

The negation of $“\forall n\in N,n+7>6”$ is ….

The negation of the statement : "Getting above $95\%$ marks is necessary condition for Hema to get the admission in good college".

Which of the following statement pattern is a tautology?

$S_1\equiv \left(~q\wedge p\right)\wedge q$

$S_2\equiv \left[p\wedge \left(p\to q\right)\right]\to q$

$S_3\equiv \left(p\wedge q\right)\wedge \left(~p\vee ~q\right)$

$S_4\equiv \left(p\wedge q\right)\to r$

Which of the following statement pattern is a tautology?

$S_1\equiv ~p\to \left(q\leftrightarrow p\right)$

$S_2\equiv ~p\vee ~q$

$S_3\equiv (p\to q)\wedge \left(q\to p\right)$

$S_4\equiv \left(q\to p\right)\vee \left(~p\leftrightarrow q\right)$

Which of the following statement is contingency?

The dual of the statement pattern $~p\wedge \left(q\vee t\right)$ is (where $t$ is a tautology and $c$ is a contradiction)