convert the compound statements into words p= babies eat bananas q= babies do not sleep through the night ~(P arrow q)
~ means not
p-> q means if p then q
Be aware that:
~(p->q) is equivalent to ~q -> ~p
What you need is:
~(if babies eat bananas, then they sleep through the night)
≡
if babies don't sleep through the night, then they do not eat bananas.
or logically
if babies don't sleep through the night, then they didn't eat bananas.
(note: the change in tense is to make it easier to understand)
dodecagon with a perimeter of 108 cm
To convert the compound statement ~(P -> q) into words, we will first translate the individual statements p and q.
p: Babies eat bananas.
q: Babies do not sleep through the night.
Now, let's break down the compound statement ~(P -> q) step by step:
1. The arrow symbol (->) represents the implication "if... then." So, we can read P -> q as "If babies eat bananas, then babies do not sleep through the night."
2. The tilde (~) symbol denotes negation. Thus, ~(P -> q) can be read as "It is not true that if babies eat bananas, then babies do not sleep through the night."
Putting it all together, the converted compound statement ~(P -> q) can be stated as "It is not true that if babies eat bananas, then babies do not sleep through the night."