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Which of the following conditions can be expressed by a Boolean formula in the Boolean variables p1,p2,p3,p4 and the connectives ∧ ∨, (without ¬ ) ?

I. At least three of p1,p2,p3,p4 are true.

II. Exactly three of p1,p2,p3,p4 are true.

III. An even number ofp1,p2,p3,p4are true.

(A) I only

(B) II only

(C) III only

(D) I and III
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2 Answers

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Statement::1

(P1 ^ P2 ^ P3 v P4) v (P1 ^ P2 ^ P4 v P3) v (P1 ^ P4 ^ P3 v P2) v (P4 ^ P2 ^ P3 v P1)

Statement::2 

NOT POSSIBLE

Statement::3

NOT POSSIBLE, but if wecan use (~) than will it be right?

(P1 ^ P2 ^ P3 ^ P4) v (P1 ^ P2 ^ ~P3 ^  ~P4) v  (P1 ^ P3 ^ ~P2 ~P4) v  (P2 ^ P3 ^ ~P1 ^  ~P4) v  (P3 ^ P4 ^ ~P1 ^  ~P2) .... v  (~P1 ^ ~P2 ^ ~P4 ^  ~P3) 

so, hre answer will be (A)

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