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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Q. Determine the truth value of statement ∃n (4n = 3n) if the domain consists of all integers.

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Q. Let Q(x, y) denote “M + A = 0.” What is the truth value of the quantifications ∃A∀M Q(M, A).

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Q. Translate ∀x∃y(x < y) in English, considering domain as a real number for both the variable.

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Q. “The product of two negative real numbers is not negative.” Is given by?

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Q. Let Q(x, y) be the statement “x + y = x − y.” If the domain for both variables consists of all integers, what is the truth value of ∃xQ(x, 4).

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Q. Let L(x, y) be the statement “x loves y,” where the domain for both x and y consists of all people in the world. Use quantifiers to express, “Joy is loved by everyone.”

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Q. Let T (x, y) mean that student x likes dish y, where the domain for x consists of all students at your school and the domain for y consists of all dishes. Express ¬T (Amit, South Indian) by a simple English sentence.

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Q. Express, “The difference of a real number and itself is zero” using required operators.

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