Matdis

#70
by awaa99 - opened

๐Ÿ˜ƒ: Write each of these propositions in the form โ€œp if and
only if qโ€ in English.
a) If it is hot outside you buy an ice cream cone, and if
you buy an ice cream cone it is hot outside.
b) Foryoutowinthecontestitisnecessaryandsufficient
that you have the only winning ticket.
c) You get promoted only if you have connections, and
you have connections only if you get promoted.
d) Ifyouwatchtelevisionyourmindwilldecay,andcon
versely.
e) The trains run late on exactly those days when I take
it.
๐Ÿค–: Sure! Here are the propositions in the form "p if and only if q" in English:

a) If it is hot outside, then you buy an ice cream cone (if-then statement). Therefore, p if and only if q.
b) It is necessary and sufficient for you to have the only winning ticket that you will win the contest (iff statement). So, p if and only if q.
c) If you get promoted, then you have connections (if-then statement). And if you have connections, then you got promoted (iff statement). Hence, p if and only if q.
d) Watching television causes your mind to decay (causal statement), and conversely, not watching television does not cause your mind to decay (negation of the antecedent). Therefore, p iff q.
e) If the train runs late, then you took it (if-then statement). However, taking the train does not guarantee that it will be late (contradictory premise). Thus, p if and only if q.

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