Prove that the following biconditional compound statement is true :
The integer x is even if and only if `x^(2)` is even .

Using the words " necessary and sufficient " rewrite the following two biconditional statements : The integer N is even if and only if N^(2) is even .

Find the validity of the following biconditional Statement. A triangle is-equilateral if and only if the angles of the triangle are equal

Find the value of each of the following compound statements : The number 12 is both prime and even .

Show that the following statement is true by the method of contrapositive : "If x is an integer and x^(2) is even , then x is also even."

Check whether the follwing compound statements is true or false . If a and b are odd integers , then (a +b) is an even integer .

Show that the following statement is true by the method of contrapositive:If x Is an integer and x^2 is even,then x is also even"

By giving a counter example show that the following compound statement is not true . "If x and y are two real numbers , then x^(2)=y^(2) implies x = y " .

Show that that the following statement are true by the method of contapositive. p:If x is an integer and x^2 is even ,then x is also even.

Write down the contrapositive of the following " if ………., then ……" implications : If x is an integer and x^(2) is even then x is even .

Rewrite each of the following compound statements with " if ……., then ……" implications : n^(2) is an even number when the number n is even .