A survey of 100 students at New England College showed the following: 46 take English. 47 take history. 38 take language. 13 take English and history. 16 take English and language. 18 take history and language. 8 take all three. How many students do the following? (See Example 6.) (a) Take history but neither of the other two? students (b) Take English and history but not language? students (c) Take none of the three? students (d) Take just one of the three? students (e) Take exactly two of the three? students (f) Do not take language? students Additional Materials MOBook

Q: Simplify the expression [(a'^b)v (av b')]v (a'nb^c) by using the laws of Boolean algebra.

A: By using laws of boolean algebra,    De Morgan's law  Double Negation Idempotent Law Absorption law…

Q: Proof by contradiction. There is no largest composite number

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Q: If U = {-1, 0, 1, 14, 16, 19}, A = {1, 14, 19}, and B = {-1, 0, 14}, find the following. (Enter your…

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Q: Prove the following statement: "Let a, b and n be integers. If n doesn't divide ab, then n doesn't…

A: The given statement is -" Let a.b and n are integers. If n doesn't divide ab, then n doesn't divide…

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Q: Find the mean for the following group of data items. 8.6, 4.8, 7.4, 6.7, 2.1, 3.1, 7.9, 4.2, 7.3,…

A: Find the mean for the following group of data items.8.6, 4.8, 7.4, 6.7, 2.1, 3.1, 7.9, 4.2, 7.3,…

Q: Prove that A CB P(A) C P(B).

A: We have to prove that

Q: 26. Let E be the set of all even integers, and let O be the set of all odd integers. Let X = {n €Z|n…

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Q: 6. There are real numbers a and b such that Tarb = √at VE Proof: Let

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Q: 4. Prove: A\ (BNC) = (A \ B) U (A \ C)

A: A\ B = A-B .

Q: QUESTION 3 Construct the Operation Table for U(15)

A: Cayley table

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Q: How many ways can three items be selected from a group of eight items?

A: Number of items = n = 8 Number of items to be chosen = r = 3

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.