Write the following compound statement in terms of the simple statements p, q, and r.

"Upper I pay the bills or take the kids to the park, or my wife is not happy.Ipaythebillsortakethekidstothepark,ormywifeisnothappy."

p:

I pay the bills.

q:

I take the kids to the park.

r:

My wife is

happy.

Question content area bottom

Part 1

a. Write the statement in symbolic form in terms of p, q, and r.

A.

(p

logical and

q)

logical and

~r

B.

(p

logical and

q)

logical and

r

C.

(p

logical or

q)

logical or

r

D.

(p

logical or

q)

logical or

~r

Your answer is correct.

E.

(p

logical or

q)

logical and

~r

F.

p

logical and

(q

logical or

~r)

Part 2

b. Construct a truth table for the symbolic statement in part (a).

Part 3

Part 4

Part 5

Part 6

Part 7

Part 8

Part 9

Part 10

p	q	r	p logical or qpq	~r	left parenthesis p logical or q right parenthesis logical or tilde r(pq)~r
T	T	T	Upper TT	Upper FF	Upper TT
T	T	F	Upper TT	Upper TT	Upper TT
T	F	T	Upper TT	Upper FF	Upper TT
T	F	F	Upper TT	Upper TT	Upper TT
F	T	T	Upper TT	Upper FF	Upper TT
F	T	F	Upper TT	Upper TT	Upper TT
F	F	T	Upper FF	Upper FF	Upper FF
F	F	F	Upper FF	Upper TT	Upper TT

Part 11

c. Use the truth table to indicate the set of all conditions on p, q, and r that make the compound statement true, or state that no such conditions exist.

A.

The statement is true whenever

p, q, and r are true,

and is false otherwise.

B.

The statement is true whenever

p or q is true or r is false,

and is false otherwise.

C.

The statement is true whenever

p, q, or r is true,

and is false otherwise.

D.

The statement is true whenever

p and q are true and r is false,

and is false otherwise.

E.

There are no conditions for which the statement is true.