USE A TRUE TABLE TO DETERMINE WHETHER THE FOLLOWING STATEMENTS ARE A TAUTOLOGY, SELF-CONTRADICTION, OR NEITHER (~p ˅ q) ↔ ~q p q (~ p ˅ q ) ↔ ~ q T T T F F T F F
USE A TRUE TABLE TO DETERMINE WHETHER THE FOLLOWING STATEMENTS ARE A TAUTOLOGY, SELF-CONTRADICTION, OR NEITHER
(~p ˅ q) ↔ ~q
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p |
q |
(~ p ˅ q ) ↔ ~ q |
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T |
T |
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T |
F |
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F |
T |
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F |
F |
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(B). (~q → p) ˅ ~q
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p |
q |
( ~ q → p ) ˅ ~ q |
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T |
T |
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T |
F |
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F |
T |
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F |
F |
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IV DETERMINE WHETHER THE STATEMENT IS AN IMPLICATION.
(p ˅ q) → (p ˅ ~r)
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p |
q |
( p ˅ q ) → ( p ˅ ~ r) |
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T |
T |
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T |
F |
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F |
T |
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F |
F |
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V IF p IS TRUE, q IS FALSE, AND r IS TRUE, FIND THE TRUTH
VALUE OF THE FOLLOWING STATEMENTS. No table required
(~p ↔ r) ˅ (~q↔ r)
VI IN THE FOLLOWING EXERCISES, WRITE THE STATEMENT IN
SYMBOLIC FORM (use p, q and r in the same order of the statement).
THEN CONSTRUCT A TRUTH TABLE FOR THE SYMBOLIC STATEMENT.
IF IT IS RAINING, THEN THE BASEBALL GAME IS CANCELED
AND WE CAN EAT DINNER TOGETHER.
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p |
q |
r |
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T |
T |
T |
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T |
T |
F |
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T |
F |
T |
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T |
F |
F |
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F |
T |
T |
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F |
T |
F |
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F |
F |
T |
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F |
F |
F |
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VII LET p REPRESENT “YOU WILL LOVE ME”
AND LET q REPRESENT “I WILL LOVE YOU.”
WRITE EACH STATEMENT IN SYMBOLS, and as specified
A). IF YOU WILL LOVE ME THEN I WILL LOVE YOU
B). IF YOU WON’T LOVE ME, THEN I WILL LOVE YOU.
C). I WON’T LOVE YOU IF AND ONLY IF YOU WON’T LOVE ME.
D). USING THE SAME STATEMENTS ABOVE, WRITE THE
FOLLOWING STATEMENT IN WORDS ~(p Ú ~q)
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