Question

Translations(use ∀ or ∃): (10 points) a) All students love MAT200 and do homework. b) Some students love MAT200 and don’t do homework. c) All Students have friends. d) Some student’s friends love MAT200. e) Some students are not friends, but they love MAT200.

Answer 1

Answer:

a) ∀ (All students love MAT200 and do homework.)

b) ∃ (Some students love MAT200 and don’t do homework.)

c) ∀ (All Students have friends.)

d) ∃ (Some student’s friends love MAT200.)

e) ∃ (Some students are not friends, but they love MAT200.)

Explanation:

∀ is a logical operator symbol for universal quantification in predicate logic.  It asserts that the property or relation holds true for all members of the domain.

∃ is a logical operator symbol for an existential quantification in predicate logic, which asserts that the property or relation holds true for some members of the domain and not for all.