Construct a Complete Truth Table for Each of the Following $\lor$

question 41

Multiple Choice

Construct a complete truth table for each of the following arguments. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
-P ≡ ∼Q
∼(Q $\lor$ ∼P)
Q ⊃ ∼Q / P

• A) Valid
• B) Invalid. Counterexample when P and Q are true
• C) Invalid. Counterexample when P is true and Q is false
• D) Invalid. Counterexample when P is false and Q is true
• E) Invalid. Counterexample when P and Q are false

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Definitions:

Hamstring Muscles

A group of three muscles located at the back of the thigh that are responsible for bending the knee and extending the hip.

Anterolateral Surface

The front and side area of an anatomical structure or body part.

Obturator Externus

A muscle situated on the outer surface of the pelvic bone which acts to rotate the thigh laterally.

Piriformis

A muscle in the gluteal region of the lower limb, involved in the rotation of the thigh and known for its relation to the sciatic nerve.