Q-1: [4+2 marks] a) Establish whether each of the following propositions is a tautology, contradiction or...

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Q-1: [4+2 marks] a) Establish whether each of the following propositions is a tautology, contradiction or contingency: i. (ab)(ab) V (a Ab), by using truth tables. ii. (p(qp)), by using laws of logic. b) Let P(x) be the statement "x is happy" and Q(x) be the statement "x is under 20", where the universe of discourse for x is the set of AOU students. Express each of the following English statement in terms of quantifiers and logical connectives: i. There is an AOU student who is happy and over 20. ii. Not all AOU students are either unhappy or under 20. Q-1: [4+2 marks] a) Establish whether each of the following propositions is a tautology, contradiction or contingency: i. (ab)(ab) V (a Ab), by using truth tables. ii. (p(qp)), by using laws of logic. b) Let P(x) be the statement "x is happy" and Q(x) be the statement "x is under 20", where the universe of discourse for x is the set of AOU students. Express each of the following English statement in terms of quantifiers and logical connectives: i. There is an AOU student who is happy and over 20. ii. Not all AOU students are either unhappy or under 20.