In lecture 5 we discussed statements that are valid and inconsistent. Are the following statements valid, inconsistent or neither? Justify your answer. (a) A+¬A (b) A+ B (c) -BABA-B (d) -A^ (Av B) ^-B
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- Homework 1. Prove Rule 11: A+ÃB = A+B. starting from the left side A+ÃB and prove it's equal to the right side A+B 2. Simplify the following Boolean expression: a. ĀBC + AB Č + ĀB Č+ ABC + ABC Ans: BC + AB + BC b. (Ā+B) (A+B+D) D Ans: BDExpress each of these mathematical statements using predicates, quantifiers, logical connectives, andmathematical operators.a) The product of two negative real numbers is positive.b) The difference of a real number and itself is zero.c) Every positive real number has exactly two square roots.d) A negative real number does not have a square root that is a real number.e) Every non-zero real number has a unique reciprocal.1- Refer to the following picture of Tarski's world. Let Above(x, y) mean that az is above y (but possibly in a different column). Determine the truth or falsity of each if the following statements. Give reasons for your answers. (a) (b) b g A f h FIGURE 3.1.1 y such that Square(y) A Above(y, d). z such that Triangle(z) A Above(f, z). d i k
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