If the Boolean expression $(p \wedge q) \circledast (p \otimes q)$ is a tautology,then $\circledast$ and $\otimes$ are respectively given by

Consider statements $p: S_1$ is closed; $q: S_2$ is closed; $r: S_3$ is closed. The simplified equivalent circuit diagram and its logical statement for the switching circuit is respectively.

Find the component statements of the following and check whether they are true or not.
$A$ person who has taken Mathematics or Computer Science can go for $MCA$.

Consider the statement: "For an integer $n$,if $n^{3}-1$ is even,then $n$ is odd." The contrapositive statement of this statement is

Given below are two pairs of statements. Combine these two statements using "if and only if".
$p:$ If a rectangle is a square,then all its four sides are equal.
$q:$ If all the four sides of a rectangle are equal,then the rectangle is a square.

Which of the following logical statements is a tautology?