QUESTION 1 Let pand r be the proposition p : You are beautiful. 9: You miss the bus. r: You go to the gym Express each of these propositions as an English sentence. a) -- QUESTION 3 Show that pq and (p Aq) (199) are logically equivalent using equations. QUESTION 4 Determine whether (up ^ (p)) -- is a tautology or not using the truth table. QUESTION 4 Show that (p)^(p-r) and p(q Ar) are logically equivalent using truth table. T T T Arial 3 (12pt) T.EE EN QUESTION 6 1 Let P(x) be the statement "x + 1 > 2x". If the domain consists of all integers, what are these truth values, and explain WHY? 1. Vx P(x) QUESTION 5 1 poir Let P(x) be the statement "x + 1 > 2x". If the domain consists of all integers, what are these truth values, and explain WHY? 1. x Px) QUESTION 7 Translate these statements into English, where H(x) is "x is an actress" and G(x) is "x is genius" and the universe of discourse consists of all people. 3x (H(x) - G(x)) _51783_1&course_id=_65136_18.content_id=_1950765_18 Question Completion Status: 20 30 4 6 7 BL QUESTION 7 Translate these statements into English, where H(x) is "x is an actress" and G(x) is "x is genius" and the universe of discourse consists of all people. 1. Vx (H(x) AG(x))