Question

[x, y, and z are integer variables, which expressions are equivalent to each other?]

a. (x==y && x !=z) || (x!=y && x==z)

b. (x==y || x==z) && (x!=y || x!=z)

c. (x==y) != (x==z)

Answer 1

We will be breaking down the following expressions similar to simple englisg statements as follows

1. (x==y && x !=z) || (x!=y && x==z)

   In this experssion we see that X is equal to Y and X is not equal to Z. Secondly we see that X is equal to

   Z but X is not equal to Y.

   Conclusion: So we can conclude that X is equal to Y |Z but not the other

   Explanation: Here we can see that in the first case When X is equal to Y it is not equal to Z and vice versa when

                       X is equal to Z then it is not equal to Y.

2. (x==y || x==z) && (x!=y || x!=z)

    In this case we see that X is equal to Y or X is equal to Z and X is not equal to Y or X is not equal to Z

Conclusion: X is eequal to one of the two values and X is not equal to one of the two values

    Explanation: Here in this Expression we see that the Left hand side is true if any one ofthe value is true and on

                       the Right Hand Side is true if any one of the value is not equal to other. but both are required to

                       true as AND operator is between them

3. (x==y) != (x==z)

      Here in this Expression we see thar in Left Hand side X is equal to Y and in the Right hand side we see that

     Xis equal to Z but the Left hand side should be complement of Right hand side and Vice Versa.

     Conclusion:So we can conclude that X is equal to Y |Z but not the other

     Explanation: In the above expression we see that If X is equal to Y then it should be equal to Z and

                        on the other side if X is equal to Z it should not be equal to Y