# (Homework Solution): (10*15 + 3.25 + 50 275 Points) 2.1 Rewrite each statement using the If… Then connective.

(10*15 + 3.25 + 50 275 Points) 2.1 Rewrite each statement using the If… Then connective. Rearrange the wording as necessary 2.1.1 Anas area code is 216 2.1.8 No pain is sufficient for no gain. 2.1.2 All Saudi Youth love El-barr camp. 2.1.7 The great leader Seif El-Din Kotoz Smashed the Tatars 2.1.9 Not observing the speed limit is necessary for getting a speeding ticket. 2.1.6 The great leader Salah El-Din got back Alkodas Alshareef from the crusaders. .1.4 Only if it is the great leader who had won all his battles, he is Khalid lbn Al-Wleed 2.1.10 Being neither hedonistic nor ascetic are necessary for following Buddha’s “Middle Way. 2.2. Find a proposition that satisfies the given condition: 2.2.1 With three variables p, q, and r that is true when p and r are true and q is false, and false otherwise. 2.2.2 With three variables p, q, and r that is true when exactly one of the three variables is true, and false otherwise 2.2.3 With three variables p, q, and r that is never true 2.3 Prove that the proposition “if it is not hot, then it is hot” is equivalent to “it is hot”.

I Just solve only 2.2

2.2.1) With three variables p,q and r that is true when p and r are true and q is false, and false otherwise

Sol) p ^ ~q ^ r

2.2.2) With three variables p,q and r that is true when exactly one of the three variables is true, and false otherwise

Sol) (p ^ ~q ^ ~r) v (~p ^ q and ~r) v (~p ^ ~q ^ r)

2.2.3) With three variables p,q and r that is never true.

Sol) (p ^ ~p) v (q ^ ~q) v (r ^ ~r)

2.3) Prove that the proposition “if it is not hot, then it is hot” is equivalent to “it is hot”

Sol) Both propositions are true when “it is hot” is true and both are false when “it is hot” is false

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