Question

"If X then Y unless Z" is represented by which of the following formulas in propostional logic?
$("\rightharpoondown ")$ is negation , "$\wedge$" is conjuntion , and "$\to$" is implication)

• A. $(X\wedge \rightharpoondown Z)\to Y$
• B. $(X\wedge Y)\to \rightharpoondown Z$
• C. $X\to (Y\wedge \rightharpoondown Z)$
• D. $(X\to Y)\wedge \rightharpoondown Z$

Answer 1

The correct option is A $(X\wedge \rightharpoondown Z)\to Y$

If X then Y unless Z is represented by
$X\to Y$ unless $Z\equiv (X\to Y)+Z$
$\equiv X{}^{\prime }+Y+Z$

Now convert the answers one-by-one into boolean form only choice (a) converts to $X{}^{\prime }+Y+Z$ as can be seen below:
$(X\wedge \rightharpoondown Z)\to Y\equiv XZ{}^{\prime }\to Y$
$\equiv \left(XZ\right){}^{\prime }+Y$
$X{}^{\prime }+Y+Z$