Logical Equivalence Exercise: In the following English sentence, \"it is not the

Question

Logical Equivalence Exercise:

In the following English sentence, "it is not the case" is meant to say that the rest of the sentence should be negated: It is not the case that I was not late to class or I missed a quiz. Such sentences are difficult to interpret, but we can apply principles of logic to improve them. Identify the simple propositions and logical operators in that sentence, express the sentence as a logical expression, apply double negation and the appropriate DeMorgan law to simplify the expression, and finally express the simplified expression in conversational English.

Explanation / Answer

"It is not the case" represents negation (~)

Let us say "I was not late to class" is 'p'. And "I missed a quiz" is 'q'.

Convert given sentence into logical expression

That is ~(p v q)

Apply De Morgans law that is true becomes false and

False becomes true, OR becomes AND and AND becomes

OR.

so ~(p v q) = ~p ^ ~q

Negation of p or q is equal to negation of p and negation of q.

~p means I was late to class.

~q means I did not miss a quiz.

Therefore the meaning of sentence in conventional English is "I was late to class and I did not miss a quiz".

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.