Answer
a) It is hot outside if and only if you buy an ice cream cone.
b) You win the contest if and only if you have the only winning ticket.
c) You get promoted if and only if you have connections.
d) Your mind decays if and only if you watch television.
e) The train runs late if and only if I take it.
Work Step by Step
To solve this problem, substitute one phrase as $p$ and the other $q$. Create the basic "p if and only if q structure using this representation and then replace the phrases to create the sentence in English. The replacements are:
a)
p - it is hot outside
q - you buy an ice cream cone
b)
p - you win the contest
q - you have the only winning ticket
c)
p - you get promoted
q - you have connections
d)
q - you watch television
p - your mind decays
e)
p - the train runs late
q - I take it
