Self-study
Most cats like to go outside to play when the temperature is above freezing. ████████ █████ ████ ███ █████ ███ ███ ██ ██ ███████ ██████ ██ █████ ███ ██████ ██ ███ ██████ ██ ████████ ███ ███████ ██████ ███████ ██ ███████ ████ ████ ███ ███ ██ ███████ ██ ██ ██ ███ ████████
Summary
Most cats like to go outside when the temperature is above freezing.
If Jamil lets his cat go outside, then at least one of his family members is outside.
If any of Jamil’s family members are outside, then it’s sunny or hot outside.
Very Strongly Supported Conclusions
If it’s not sunny and it’s not hot, Jamil’s family members are not outside.
If it’s not sunny and it’s not hot, Jamil’s cat is not outside.
If Jamil lets his cat out, then it’s sunny or hot.
15.
Which one of the following ███ ██ ████████ ████████ ████ ███ ███████████ ██████
a
If Jamil's cat ██ ████████ ████ ███ ███████████ ██ █████ █████████
Unsupported. If Jamil’s cat is outside, then one of his family members is outside. And if one of his family members is outside, then it’s sunny or hot. Jamil’s family member and his cat could be outside when it’s below freezing but still sunny.
b
If Jamil's cat ██ ███ ████████ ██ ██ ██████ ███ ██ ██ ███ ███ ████████
Unsupported. If Jamil’s cat is outside, then it’s sunny or hot outside. But the fact that his cat is not outside tells us nothing about whether it’s sunny or hot. It’s possible that it is sunny or hot outside, but Jamil just didn’t want to let his cat out.
c
If the sun ██ ███████ ██ ██ ██ ███ ████████ ███████ ███ ██ ████████ ████████
Unsupported. “Sunny or hot” is not a sufficient condition for anything. We know that Jamil’s family members (and thus his cat) will only be outside when it’s sunny or hot. But the fact that it’s sunny or hot tells us nothing about whether his family members or his cat are out.
d
If at least ███ ██████ ██ ███████ ██████ ██ ████████ ████ ███████ ███ ██ ███████ █████
Unsupported. If at least one family member is outside, then it’s sunny or hot outside. This doesn’t necessarily mean that the cat is also outside. We just know that if the cat is out, then at least one family member is also out. (D) gets this backward.
e
If the sun ██ ███ ███████ ███ ██ ██ ███ ███ ████████ ███████ ███ ██ ███ ████████
Very strongly supported. By taking the contrapositive of the conditional chain below, we see that if it’s not sunny or hot, then Jamil’s family members aren’t outside. And if they’re not outside, then Jamil won’t let his cat out. So if it’s not sunny or hot, his cat can’t be out.
