Q. What are the contrapositive of the conditional statement “Medha will find a decent job when she labour hard.”?

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Q. What are the inverse of the conditional statement “If you make your notes, it will be a convenient in exams.”

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Q. The compound propositions p and q are called logically equivalent if ________ is a tautology.

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Q. p → q is logically equivalent to ________

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Q. p ∨ q is logically equivalent to ________

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Q. ¬ (p ↔ q) is logically equivalent to ________

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Q. p ∧ q is logically equivalent to ________

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Q. Which of the following statement is correct?

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Q. p ↔ q is logically equivalent to ________

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Q. (p → q) ∧ (p → r) is logically equivalent to ________

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Q. (p → r) ∨ (q → r) is logically equivalent to ________

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Q. Let P (x) denote the statement “x >7.” Which of these have truth value true?

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Q. Let Q(x) be the statement “x < 5.” What is the truth value of the quantification ∀xQ(x), having domains as real numbers.

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Q. Determine the truth value of ∀n(n + 1 > n) if the domain consists of all real numbers.

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Q. Let P(x) denote the statement “x = x + 7.” What is the truth value of the quantification ∃xP(x), where the domain consists of all real numbers?

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Q. Let R (x) denote the statement “x > 2.” What is the truth value of the quantification ∃xR(x), having domain as real numbers?

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Q. The statement,” Every comedian is funny” where C(x) is “x is a comedian” and F (x) is “x is funny” and the domain consists of all people.

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Q. The statement, “At least one of your friends is perfect”. Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people.

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Q. ”Everyone wants to learn cosmology.” This argument may be true for which domains?

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Q. Let domain of m includes all students, P (m) be the statement “m spends more than 2 hours in playing polo”. Express ∀m ¬P (m) quantification in English.

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