3

Notation

w,x,y,z are all just primary statements

"+" is the OR logical operator

what looks like two or more statements being multiplied is actually the AND operator

The complement or prime notation indicates the statement has been negated

"=" indicates logical equivalence

My Work

1) $w'x'z' + xy'z + wx$ (premise)

2) $w'x'z'(y'+y) + xy'z + wx$ (By Complement Law and Identity Law)

3) $w'x'y'z' + w'x'yz' + xy'z + wx$ (By Distributive Law)

4) $w'x'y'z' + w'x'yz' + xy'z + wx(y' + y)$ (By Complement Law and Identity Law)

5) $w'x'y'z' + w'x'yz' + xy'z + wxy' + wxy$ (By Distributive Law)

My Question

I feel I'm very close, but I can't think of a way to change $wxy'$ into $wxy'z'$. I tried ANDing it by $z'+z$ but that creates an extra compound statement that I don't know how to deal with. Can anyone give me a hint as to how to transform $wxy'$ into $wxy'z'$ or suggest another way to finish my proof?

Dunka
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1 Answers1

1

Suggestion:

  • Substitute $\;wxy' = wxy'z' + wxy'z\;$
  • then look for a way to absorb $\;w\color{navy}{xy'z}\;$ into something else.
Graham Kemp
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