Question

Which statement would produce a tautology? A: P^~Q B:PVQ C: PV~Q D: QV~P

Answer 1

Answer: None

Step-by-step explanation:

In order to find which statement would produce a tautology, we can use truth tables. Tautology is when the outcome is always true, or all true.

Note: ~ is the same as ¬. For clarity purposes, I will use ¬. It's hard to create a table on Brainly, so pretend the lines are all connected.

A: P∧¬Q

P  |  Q  |  ¬Q  |  P∧¬Q

T  |  T  |    F    |     F

T  |  F  |    T    |     T

F  |  T  |    F    |     F

F  |  F  |    T    |     F

This is not tautology.

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B. P∨Q

P  |  Q  |  P∨Q

T  |  T  |    T

T  |  F  |    T

F  |  T  |    T

F  |  F  |    F

This is not tautology.

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C. P∨¬Q

P  |  Q  |  ¬Q  |  P∨¬Q

T  |  T  |    F   |     T

T  |  F  |    T   |     T

F  |  T  |    F   |     F

F  |  F  |    T   |     T

This is not tautology.

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D. Q∨¬P

Q  |  P  |  ¬P  |  Q∨¬P

T  |  T  |    F   |     T

T  |  F  |    T   |     T

F  |  T  |    F   |     F

F  |  F  |    T   |     T

This is not tautology.

Now, we know that none of these statements would produce a tautology.