Logic Worksheet With Answers Page 13
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22p if and only if q: p q and q p
p q
p
q
T
T
T
T
F
F
F
T
F
F
F
T
The Biconditional is True only when the component statements have the same value.
Ex: You receive a letter that states that you have been assigned a Prize Entry Number –
88855566. If your number matches the winning pre-selected number and you return the number
before the deadline, you will win $1,000,000.00.
Suppose that your number does not match the winning pre-selected number, you return the
number before the deadline and only win a free issue of a magazine. Under these conditions, can
you sue the credit card company for making a false claim?
Assign letters to the simple statements in the claim;
p: Your number matches the pre-selected number
False
q: You return the number before the deadline
True
r: You win the prize
False
Write the underlined claim in the letter in symbolic form: (pq) r.
Substitute the truth values for p, q, and r to determine the truth value for the letter’s claim:
(FT) F, so we have F F which is True.
The truth-value analysis indicates that you cannot sue the credit card company for making a false
claim.
Part 5: Equivalent Statements and Variation of Conditional Statements
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