Question

For table shown in figure 1 construct (a) a Boolean expression having the given table as...

For table shown in figure 1 construct (a) a Boolean expression having the given table as its truth table and (b) a circuit having the given table as its input/output table. (10 points) Figure 1: Truth table 6. Find the Boolean expressions for the circuits in figure 2 and show that they are logically equivalent when regarded as statement forms.(16 points) Figure 2: Circuits 7. Let R(m, n) be the predicate “If m is a factor of n 2 then m is a factor of n” with domain for both m and n being the set Z of integers. (8 points) (a) Explain why R(m, n) is false if m = 25 and n = 10. (b) Give values different from those in part (a) for which R(m, n) is false. (c) Explain why R(m, n) is true if m = 5 and n = 10. (d) Give values different from those in part (c) for which R(m, n) is true. 8. Rewrite the following statements in formally. Also write a formal negation for each statement. Use quantifiers and variables. (8 points) (a) For any isosceles triangle T , the base angles of T are equal. (b) There exists a continuous function f such that f is not differentiable. (c) c is any computer. c has a cpu. (d) There exists a band b such that b has won at least 10 Grammy awards.

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