onsider the following Boolean expressions (A OR C) AND(B AND C) A AND (B AND C)
ID: 3611512 • Letter: O
Question
onsider the following Boolean expressions(A OR C) AND(B AND C)
A AND (B AND C)
Prove that these two Boolean expressions are not equivalent byfinding a value of A, a value of B and a value of C such that thetwo expressions take different truth values when A,B,C are assignedthe values u have found.
please give a thourough explanation of your steps
Explanation / Answer
e1 = (A OR C) AND(B AND C) e2 = A AND (B AND C) This can be proved by finding the above expression values for eachvalues of A,B and C. Here we will use the two Bitwise operator: AND Truth table for AND 0 0 -> 0 0 1 -> 0 1 0 -> 0 1 1 -> 1 OR Truth table for OR 0 0 -> 0 0 1 -> 1 1 0 -> 1 1 1 -> 1 now using above tables , we put the different value of A,B, and C,we get. A B C (A OR C) AND(B ANDC) A AND (B AND C) 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 1 so form above table we can see that when A=0 B=1 C= 1 then e1= 1, and e2 = 0, so these value of A,B,C are 0,1,1respectively, when both expression are different.
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