Answer
Converses:
a. If P is a rectangle then P is a square
b. If tomorrow is January, then today is New Year's eve.
c. If r is rational, then the decimal expansion of r is terminating.
d. If n is odd or if n is 2, then n is prime
e. If x is positive or if x is 0, then x is non-negative
f. If Jim is Ann;s uncle and Sue is her aunt, then Tom is her father
g. If n is divisible by 2 and n is divisible by 3, then n is divisible by 6
Inverses:
a. If P is not a square then P is not a rectangle
b. If today is not New Year's eve, then tomorrow is not January.
c. If the decimal expansion of r is not terminating, then r is not rational.
d. If n is not prime, then n is not odd and is not equal to 2
e. If x is not non-negative, then x is not positive and if x is not 0
f. If Tom is not Ann's father, then Jim is nother uncle or Sue is not her aunt
g. If n is not divisible by 6, then n is not divisible by 2 or n is divisible by 3
Work Step by Step
Converse of the statement p → q is q → p
Inverse of the statement p → q is ~p → ~q
Note that even if the statement is true, the inverse and the converse may not be true.
Also not that ~(q and r) ≡ ~q or ~r
And that, ~(q or r) ≡ ~q and ~r
