Question

Write the inverse, converse, contrapositive, and biconditional of the conditional statements. determine their truth value. if false, explain or give counterexample. if a number is a natural number, then is it also a whole number.

Answer 1

Explanation:

Given conditional:

→ If a number is a natural number, then is it also a whole number.

If P then Q.

P= "a number is a natural number"-hypothesis

Q="is it also a whole number"-conclusion

Inverse negates both the hypothesis P and the conclusion Q.

If not P then not Q.

→ If a number is not a natural number, then is it also not a whole number.

Converse interchanges hypothesis P for the conclusion Q.

If Q then P.

→ If a number is a whole number, then is it also a natural number.

Contrapositive interchanges hypothesis for the conclusion of the inverse

or negates both the hypothesis and conclusion of converse.

If not Q then not P.

→ If a number is not a whole number, then is it also not a natural number.

Biconditional

P if and only if Q

→ A number is a natural number if and only if is it also a whole number.