1. Is it possible for one of()and()to be true and the other false? (If not, then the associative property holds for conjunction.) [Score: 5 points]

Yes

No

2.Is it possible for one of()and()to be true and the other false? (If not, then the associative property holds for disjunction.) [Score: 5 points]

Yes

No

3.Is it possible for one of()and()()to be true and the other false? (If not, then the distributive property holds for conjunction across disjunction.) [Score: 5 points]

Yes

No

4.Is it possible for one of()and()()to be true and the other false? (If not, then the distributive property holds for disjunction across conjunction.) [Score: 5 points]

Yes

No

5.Is showing that the negationis true equivalent to showing thatis false? [Score: 5 points]

Yes

No

6.Assuming you know nothing more about Alice, which of (a) - (e) is most likely? (Or does (f) hold?) (a) Alice is a rock star and works in a bank.

(b) Alice is quiet and works in a bank.

(c) Alice is quiet and reserved and works in a bank.

(d) Alice is honest and works in a bank.

(e) Alice works in a bank.

(f) None of the above is more or less likely.

7.Assuming you know nothing more about Alice, which of (a) - (e) is most likely? (Or does (f) hold?)

(a) Alice is a rock star or she works in a bank.

(b) Alice is quiet and works in a bank.

(c) Alice is a rock star.

(d) Alice is honest and works in a bank.

(e) Alice works in a bank.

(f) None of the above is more or less likely.

8.Question 8

Identify which of the following are true (wherexdenotes an arbitrary real number). If you do not select a particular statement, the system will assume you think it is false.

(x>0)(x10)means0x10

(x0)(x2<9)means0x<3

(x0)(x0)meansx=0

There is noxfor which(x<4)(x>4)

5x5meansxis at most 5 units from 0.

5

(x0)(x<0)

(0=1)(x20)

If(x>0x<0)thenx0.

Ifx2=9then(x=3x=3).