For each of the following compound statements,first identify the corresponding component statements. Then check whether the statements are true or not.
If a triangle $ABC$ is equilateral,then it is isosceles.

By giving a counterexample,show that the following statement is not true.
$p:$ If all the angles of a triangle are equal,then the triangle is an obtuse-angled triangle.

Given $p$: $A$ man is a judge,$q$: $A$ man is honest. If $S_1$: If a man is a judge,then he is honest; $S_2$: If a man is a judge,then he is not honest; $S_3$: $A$ man is not a judge or he is honest; $S_4$: $A$ man is a judge and he is honest. Then:

The simplified switching circuit for the following circuit is

The negation of the statement "$2 + 3 = 5$ and $8 < 10$" is:

$ \sim[(\sim p) \wedge q] $ is logically equivalent to