Solved: Given three sets A, B, and C. Suppose we know that the union of the three sets has cardinality 182. Further, |A| = 92, |B| = 41, |C| = 118. Also, |A ∩ B| = 15, |A ∩ C| = 42, and |A ∩ B ∩ C| = 10. Find |B ∩ C|.

Q 4: Find the Number of Mathematics students in a university taking at-least one of the language Mandarin, English and Japan Give the following data: 65 study Mandarin 45 study English 42 study Japanese 20 Study Mandarin and English …

6. Use truth tables to determine whether the argument form is valid. [5 Marks] a. There is an undeclared variable or there is a syntax error in the ﬁrst ﬁve lines. b. If there is a syntax error in the ﬁrst ﬁve lines, then there is a m…

∀x∃y(x + y = 2 ∧ 2x − y =1

A palindrome number is a number that is read similarly backwards. How many possible 5-digit palindromic numbers are there? A. 608 B. 648 C. 688 D. 728

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There are 7 groups in a picnic who have brought their own lunch box, and then the 7-lunch boxes are exchanged within those groups. Determine the number of ways that they can exchange the lunch box such that none of them can get their …

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Let ρ be a relation on a set A. Define ρ −1 = { | ∈ ρ}. Also for two relations ρ, σ on A, define the composite relation ρ ◦ σ as (a, c) ∈ ρ ◦ σ if and only if there exists b ∈ A such that ∈ ρ and ∈ σ. Prove the following assertions (a…

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The Mathclub, VIT-AP wants to conduct a group event for its members. So the club president has to fix the group size the event. When he tries to fix the size to be 5 members in each group, 4 members are left; when he tries to fix the …

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Given three sets A, B, and C. Suppose we know that the union of the three sets has cardinality 182. Further, |A| = 92, |B| = 41, |C| = 118. Also, |A ∩ B| = 15, |A ∩ C| = 42, and |A ∩ B ∩ C| = 10. Find |B ∩ C|.

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