Boolean function

### Question

Which of the following are correct for `F(x, y, z) = xyz + x(yz)' + x'(y + z) + (xyz)` I’m not going to give the answers cause it is on the test

### What I’ve tried

so when i worked each answer out they are all true for at least one of the aspects of the expression, and because they are all behind or gates and not and gates if one part of it works it should work for the function but when i put that they should all work it says wrong. so im just looking for some help and the right direction on this one.

Hey,
I think you might want to include a screenshot and/or the solutions, so that anyone wanting to help could have more context.

Its a simplification question. Remember the Boolean identities.

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Sorry about my first reply, I sort of had your question confused with someone else’s. If I remember correctly, the answer choices involved multiple configurations, ex(0, 0, 1), (1, 0, 0) etc., with the expression equal to either 0 or 1? If this is the case, substitute the variable with the number (0/false or 1/true) it represents, and the opposite if the ‘not’ symbol is over the variable. Once you do that, you should be able to “do the math” and simplify the problem to one final solution (1 or 0).

The tricky part is remembering the difference between TRUE and CORRECT. As a result, some equations will not be TRUE (not 1 or =0) but be correct. As long as the variables provided equal the solution when plugged in and simplified, it should be correct (the math checks out).

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thanks for the feedback i was missing the correct vs true ( just had true on the brain) i am going to share just to get the feedback before i submit again

Remember that even though you might end up with (0+0+1+1) that will equal 1, not 2. 1 just means “true”, so the solution can never be higher than 1 (true or false = 1 or 0). That said, the first solution set will produce 1 as the answer, which makes it incorrect. You would apply that to the other sets.

3 Likes

thank you! Your responses helped me a ton!

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Hello. I’m having the same road block. The solution sets do change order after each submittal. Can you confirm which set you are mentioning here. Would help confirm if I’m following the right steps. I’m on my last chance to submit perfect score and this problem has taken my other 3 tries. Thanks.

Cancel. I got it. Plugged in values 3 times and got same answer each time. Just needed to be comfortable with answers. Just completed tech assessments and I’m accepted. Thanks!

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I’m very happy for you. Some of this stuff can be extremely tricky.