Answer to Question #315991 in Discrete Mathematics for Pravin

Question

Give the inverse, converse and contrapositive for each of the following propositions.

a) If x + y = 1 then x2 + y2 ≥ 1

b) If 2 + 2 = 4 then 3 + 3 = 8

Answer 1

a) inverse: If $x+y\not=1$ , then $x^2+y^2<1$

converse: if $x^2+y^2≥1$ , then x + y = 1

contrapositive: If $x^2+y^2<1$ , then $x+y\not=1$

b) inverse: If $2+2\not=4$ , then $3+3\not=8$

converse: if $3+3=8$ , then 2+2=4

contrapositive: If $3+3\not=8$ , then $2+2\not=4$