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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Q. Use quantifiers and predicates with more than one variable to express, “There is a pupil in this lecture who has taken at least one course in Discrete Maths.”

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Q. Determine the truth value of ∃n∃m(n + m = 5 ∧ n − m = 2) if the domain for all variables consists of all integers.

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Q. Find a counter example of ∀x∀y(xy > y), where the domain for all variables consists of all integers.

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Q. Which rule of inference is used in each of these arguments, “If it is Wednesday, then the Smartmart will be crowded. It is Wednesday. Thus, the Smartmart is crowded.”

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Q. Which rule of inference is used in each of these arguments, “If it hailstoday, the local office will be closed. The local office is not closed today. Thus, it did not hailed today.”

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Q. Which rule of inference is used, ”Bhavika will work in an enterprise this summer. Therefore, this summer Bhavika will work in an enterprise or he will go to beach.”

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Q. What rule of inference is used here?

“It is cloudy and drizzling now. Therefore, it is cloudy now.”

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Q. What rule of inference is used in this argument?

“If I go for a balanced diet, then I will be fit. If I will be fit, then I will remain healthy. Therefore, if I go for a balanced diet, then I will remain healthy.”

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Q. What rules of inference are used in this argument?

“All students in this science class has taken a course in physics” and “Marry is a student in this class” imply the conclusion “Marry has taken a course in physics.”

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Q. What rules of inference are used in this argument?

“It is either colder than Himalaya today or the pollution is harmful. It is hotter than Himalaya today. Therefore, the pollution is harmful.”

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Q. The premises (p ∧ q) ∨ r and r → s imply which of the conclusion?

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Q. What rules of inference are used in this argument?

“Jay is an awesome student. Jay is also a good dancer. Therefore, Jay is an awesome student and a good dancer.”

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