Using the words ''necessary and sufficient'' rewrite the statement ''The integer n is odd if and only if `n^(2)` is odd''. Also check whether the statement is true.

Let P(n) be the statement: " n^(3)+n is divisible by 3." i. Prove that P(3) is true. ii. Verify whether the statement is true for n = 4.

Check whether''Or'' used in the following compound statement is exclusive or inclusive? Write the component statements of the compound statements and use them to check whether the compound statement is true or not. Justify your answer. t: you are wet when it rains or you are in a river.

In an n-type silicon , which of the following statements is true ?

Consider the statement " sqrt5 is a rational number or an irrational number". i. Find the component statements and check whether they are true or false. ii. Check whether the compound statement is true or false.

In a n-type semiconductor , which of the following statement is true?

Let P(n) denote the statement that n^(2)+n is odd. It is seen that P(n) = P(n + 1). P(n) is true for all.

Write the negation of the following statements and check whether the resulting statements are true, Australia is a continent.

Write the negation of the following statements and check whether the resulting statements are true, The sum of 3 and 4 is 9.