Please answer with solution Consider the following argument:If I am either sleeping well or doing my assignments, then I will pass the GMathcourse,I am sleeping well but I am not doing my assignments.Hence, I will not pass the GMath courseLet p = "I am sleeping well.", q = "I am doing my assignments.", and r = "I will passthe GMath course."Which of the following symbolic forms represents the hypothesis (or the conjunctionof the premises) in the given argument?I(p^q) → r] ^ (p V ~q)[(p v q) → r] ^ (p v~q)O Option 1O Option 2[(p^q) → r]^ (p ^~q)[(p v q) → r] ^ (p A~q)O Option 3O Option 4Assume that p and g are true statements and that r is a false statement. Which ofthe following statements is NOT true? *(p^q) Vr(1A b) v dOption 1Option 2~p → (~q vr)P+ (q ^r)Option 3Option 4 What are the truth values of x and y respectively ifthe compound proposition x → (x → y) is false?Suppose p is true, q is true, r is true, s is false. Find the truth value of(~p V s) V (s ^ r)Both FalseTrueBoth TrueFalseFalse and TrueTrue and FalseGiven p → q, which of the following statement/s is or are correct about itsSuppose p is false, q is false, s is true. Find the truth value oftransformation?(s V p) ^ (q ^ ~s)i. If the given conditional statement is true then its converse, q → p, may perhapsTruebe true.Falseii. The inverse of a given conditional statement is the logical negation of the givenconditional statement; that is, ~(p → q) = ~p → ~q.iii. The contrapositive, ~q → ~p, is the converse of the inverse of the givenconditional statement.i and ii onlySuppose p is true, q is true, r is false, s is false. Find the truth value of(s V p) ^ (~r V ~s)ii onloyTrueO ii onlyFalseO i, ii, and iii

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Consider the following argument: If I am either sleeping well or doing my assignments, then I will pass the GMath course. Iam sleeping well but I am not doing my assignments. Hence, I will not pass the GMath course Let p = "I am sleeping well.", q = "I am doing my assignments.", and r = "I will pass the GMath course." Which of the following symbolic forms represents the hypothesis (or the conjunction of the premises) in the given argument?