Translate the following statement into symbols. Then construct a truth table for the compound statement and indicate under what conditions the compound statement is true.

You

took out the trash

or

you did not leave the

car

a mess.

p: You

took out the trash.

q: You left the

car

a mess.

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Part 1

Write the compound statement in symbolic form and complete the truth table below.

p q	p logical or tilde qp~q
T T	T
T F	T
F T	F
F F	T

Part 2

Use the truth table to determine the set of conditions that make the compound statement true. Choose the correct answer below.

A.

The statement is true whenever

p is true or q is false,

and is false otherwise.

B.

The statement is true whenever p and q are both true, and is false otherwise.

C.

The statement is true whenever

p is false and q is true,

and is false otherwise.

D.

The statement is true whenever p and q are both false, and is false otherwise.

E.

The statement is true whenever p is true or q is true, and is false otherwise.