CSTS-SEU-KSA Discrete mathematics- Math150 Assignment 1 1st semester 2016-2017 ------------------------------------------------------------------------------------------Section I (1 mark for each) Determine whether the statement is true (T) or false (F). 1) The statement \"where are you?\" is proposition. 2) The conjunction of propositions p and q is denoted by (p q). 3) The AND function is Boolean multiplication and the OR function is Boolean addition. 4) The number of Boolean functions of degree 2 is equal to 16. 5) The statement P(x) is said to be the value of the propositional function P at x. 6) x P(x) asserts P(x) is true for some x in the domain. 1 2 3 4 5 Section II Choose the correct answer 1) The inverse of the statement q r a) q r b) q r c) r q d) r q 1 is 6 (1 mark for each) CSTS-SEU-KSA 2) Assume that p q is true then a) Exactly one of p and q must be true b) Both of p and q must be true c) No one of p and q must be true d) Both of p and q must be false 3) Boolean expression for the Boolean function F(x, y) which defined by the table below is 0 0 1 1 a) b) c) d) F( , ) 0 1 1 0 0 1 0 1 4) The Boolean expression a) b) c) 1 d) is equal to 5) Let Px, y denote "x y 1", the truth values of the quantifications yxPx, y and xyPx, y are a) Tand T b) Tand F c) F and T d) F and F 2 CSTS-SEU-KSA 6) The correct translation of the sentence \"Some student in this class has taken a course in Math.\" into predicate logic is a) xMx b) xMx c) x Mx d) x Mx 1 2 3 4 5 Section III 6 (3 marks for each) Solve the following questions 1) Construct a truth table for the proposition (p q) (q r) (p r), then show that it is a tautology. 2) Find the output of the following combinatorial circuit 3 CSTS-SEU-KSA 3) Express the statement \"If a person is male and is a parent, then this person is someone's Father\" as a logical expression involving predicates, quantifiers where the domain is all people 4) What is the truth value of xP(x), where P(x) is the statement \" x3 > 28\" and the domain consists of all positive integers not exceeding 6? 5) Find the sum-of-products expansions of the Boolean functions F ( , )= . 6) By using a truth table, Show that x + y = (x y) (x y). 4