A Consumer Advocacy Group Rates the Quality of a Cellular $A \cap B \cap C$

question 111

Essay

A consumer advocacy group rates the quality of a cellular service provider using three criteria. A: Service is available at least 99% of the time. B: Reception is clear at least 95% of the time. C: Fewer than 5% of its customers have complaints about the quality of service. a. Describe the event represented by $A \cap B \cap C$ .
b. Describe the event represented by $A \cup B \cup C$ .

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Definitions:

Modus Ponens

A valid form of argument in which if a conditional statement ("if P then Q") is accepted, and P is asserted to be true, then Q necessarily follows.

Modus Tollens

A logical argument form where the contrapositive of a premise is used to infer the negation of the hypothesis.

Hypothetical Syllogism

A logical argument composed of two conditional statements and a conclusion, based if the first premise is true, then the second one follows.

Modus Ponens

A valid form of argument in which if a conditional statement (“if p then q”) and its antecedent (“p”) are true, then the consequent (“q”) is also true.