If `w` is FALSE, `x` is FALSE, and `y` is TRUE, what is `((x OR y) AND (y AND w)') OR (x AND y' AND w')`?

Question

My thought process: x or y = true and y and w = false

false

or

x and not y = false and false = false and true

false = false ?

I'm not sure where I'm wrong here.

Answer 1

I'm not sure exactly where you went wrong because you haven't expressed the working clearly. But here's what I get.

If w is FALSE, x is FALSE, and y is TRUE, what is ((x OR y) AND (y AND w)') OR (x AND y' AND w')?

((x OR y) AND (y AND w)') OR (x AND y' AND w')

Replace suffix ' with prefix NOT ... 'cos I think it is clearer

((x OR y) AND NOT (y AND w)) OR (x AND NOT y AND NOT w)

Substitute values for variables

((FALSE OR TRUE) AND NOT (TRUE AND FALSE)) OR (FALSE AND NOT TRUE AND NOT FALSE)

Reduce

((TRUE) AND NOT (FALSE)) OR (FALSE AND FALSE AND TRUE)

Reduce

(TRUE AND TRUE) OR (FALSE)

Reduce

TRUE OR FALSE

Reduce

TRUE

Lesson: show your complete working, like they told you in your math classes.