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Math  /  Discrete

QuestionLet p,qp, q, and r represent the following simple statements. p : It is Tuesday. q : This is an octopus. r . I get an A. Write the symbolic statement in words. ∼r→(q∧p)\sim r \rightarrow(q \wedge p)
Choose the correct answer below. A. If I do not get an A, then this is not an octopus and it is Tuesday. B. If I get an A then this is an octopus, and it is Tuesday. C. If I do not get an A, then this is an octopus and it is Tuesday. D. If I get an A then this is not an octopus, and it is not Tuesday.

Studdy Solution

STEP 1

1. p p represents the statement "It is Tuesday."
2. q q represents the statement "This is an octopus."
3. r r represents the statement "I get an A."
4. The symbolic statement is ∼r→(q∧p)\sim r \rightarrow (q \wedge p).

STEP 2

1. Interpret the symbolic logic statement.
2. Translate the symbolic logic into words.
3. Match the translation to the given options.

STEP 3

The symbol ∼r\sim r represents the negation of r r , which translates to "I do not get an A."
The symbol →\rightarrow represents a conditional statement, which translates to "If...then..."
The symbol q∧p q \wedge p represents a conjunction of q q and p p , which translates to "This is an octopus and it is Tuesday."

STEP 4

Translate the symbolic statement ∼r→(q∧p)\sim r \rightarrow (q \wedge p) into words:
"If I do not get an A, then this is an octopus and it is Tuesday."

STEP 5

Compare the translated statement with the given options:
A. If I do not get an A, then this is not an octopus and it is Tuesday. B. If I get an A then this is an octopus, and it is Tuesday. C. If I do not get an A, then this is an octopus and it is Tuesday. D. If I get an A then this is not an octopus, and it is not Tuesday.
The correct answer is option C.
The correct answer is:
C \boxed{\text{C}}

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