Construct a Complete Truth Table for Each of the Following

question 54

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.)
-S
∼T • U / ∼(T • U) • S

• A) Valid
• B) Invalid. Counterexample when T, U, and S are true
• C) Invalid. Counterexample when T and S are true and U is false
• D) Invalid. Counterexample when U and S are true and T is false
• E) Invalid. Counterexample when S is true and T and U are false

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Definitions:

Sperm

The male reproductive cell or gamete, which is capable of fertilizing a female's ovum to produce offspring.

Cell

The smallest structural and functional unit of an organism, typically microscopic and consisting of cytoplasm and a nucleus enclosed in a membrane.

Rubella

A contagious viral infection, also known as German measles, characterized by a distinctive red rash.

Birth Defect

A physical or biochemical abnormality present at birth that can lead to mental or physical disabilities.