Often a question will say whether each input is true or false and then ask you to evaluate the overall output and come up with a single true or false answer. In this case, let’s try evaluating the answer for:

x = true, y = false, z = true

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The brackets work the normal way – you start from the
expression inside the innermost brackets and work your way outwards. The _{} one becomes _{}, which we know
is *false* – _{}.

The _{} expression becomes _{}. This is an OR
statement, so if *any* of the statements are true, then the whole thing is
true. In this case we’ve got two true statements in it, so the whole thing
becomes true – _{}.

The _{} is an AND statement. This means
that *all* the statements have to be true for the whole thing to be true.
Otherwise the whole thing is false. In this case, we’ve got _{} – all the
elements are true. So the whole thing is going to be true – _{}. So we can
simplify it a bit down to this:

_{}

Now there are only a couple more steps. First simplify
the bit inside the left brackets. We’ve got _{}. Since there are no brackets
around this, we can do it in any order, I’m going to do it from left to right.
So first the _{} bit
– this is an AND connector, so the outcome is *false*. So we get:

_{}

Now we deal with the second AND statement – the outcome
of this is *false* as well:

_{}

So that’s simplified the left square brackets down to a single ‘false’. We’ve got one last step:

_{}

This is an OR statement, so we only need one of the statements to be true for the whole thing to be true. So the overall answer is ‘true’:

_{}

Here’s a summary of how it went down:

_{}