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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Q. “Parul is out for a trip or it is not snowing” and “It is snowing or Raju is playing chess” imply that __________

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Q. Let the statement be “If n is not an odd integer then square of n is not odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “(square of n) is not odd.” For direct proof we should prove _________

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Q. Which of the following can only be used in disproving the statements?

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Q. Let the statement be “If n is not an odd integer then sum of n with some not odd number will not be odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “sum of n with some not odd number will not be odd.” A proof by contraposition will be ________

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Q. When to proof P→Q true, we proof P false, that type of proof is known as ___________

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Q. In proving √5 as irrational, we begin with assumption √5 is rational in which type of proof?

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