Section 2.1

4. (a) This is a proposition with truth value ''False.''

(b) This is a proposition with truth value ''True.''

(c) This is not a proposition, since the truth of the statement depends on the value assigned to $x$.

(d) This is a proposition with truth value ''False.'' (Both $x=0$ and $x=1$ work.)

(e) This is not a proposition, since the truth of the statement depends on the values assigned to $x,y$ and $z$.

(f) This is a proposition with truth value ''False.'' (Consider the case where $x=0$.)

(g) This is a proposition with truth value ''True.''

6. (a) $r\rightarrow q$

(b) If I am rich, then I am smart.

(c) If $x=0$ or $x=1$ then $x^{2}=x$.

(d) If $2+4=8$ then $2+2=4$.

7. (a) MATH

(b) If I am not rich, then I am not smart.

(c) If $x\neq 0$ and $x\neq 1$ then $x^{2}\neq x$.

(d) If $2+4\neq 8$ then $2+2\neq 4$.

12. (a) The case where $n=4$ provides a counterexample since MATH is not prime.

(b) The case where $n=3$ provides a counterexample since MATH is not prime.

(c) The case where $n=7$ provides a counterexample since MATH is not prime.

13. The case where MATH provides a counterexample since $1>-2$ but MATH

17. (a) If you touch those cookies, then I will spank you.

(b) If you touch those cookies, then you will be sorry.

(c) If you don't leave, then I will set the dog on you.

(d) If you will then I will.

(e) If you don't stop that, then I will go.

18. (a) If I don't spank you, then you are not touching (did not touch) those cookies.

(b) If you are not sorry, then you are not touching (did not touch) those cookies.

(c) If I have not set the dog on you, then you are leaving (have left).

(d) If I won't, then you won't.

(e) If I stay, then you have stopped doing that.

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