GATE Computer Science Engineering(CSE) 2027 Test: Discrete Mathematics

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

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.

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

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

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.”

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.

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.”

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.”

What rule of inference is used here? “It is cloudy and drizzling now. Therefore, it is cloudy now.”

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.”

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

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

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

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

A proof covering all the possible cases, such type of proofs are known as