2.6. Variants of Universal Conditional Statements. Consider a statement of the f

Question

2.6. Variants of Universal Conditional Statements. Consider a statement of the form: Va E D, if P(z) then Q( Its contrapositive is the statement Vx E D, if Q(x) then ~ P(x) Vx E D, if Q(x) then P(r) Its converse is the statement Its inverse is the statement VEE D, if ~P then~Q(x) 2.7. In Class Work. Write the contrapositive, converse, and inverse of the following statement If a real number is greater than 2, then its square is greater than 4 Show that a universal conditional statement is logically equivalent to its contrapositive. Show that a universal conditional statement is NOT logically equivalent to its converse. Show that a universal conditional statement is NOT logically equivalent to its inverse.

Explanation / Answer

Given statement

If a real number is greater than 2, then it's square is greater than 4.

Contrapositive of the given statement,

If square of a real number is not greater than 4, then the number is not greater than 2.

Or, If square of a real number is less than or equal to 4, then the number is less than or equal to 2. (Answer)

Converse of the given statement,

If square of a real number is greater than 4, then the number is greater than 2. (Answer)

Inverse of the given statement,

If a real number is not greater than 2, then it's square is not greater than 4. (Answer)

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