Logic circuit assessment question

Im a bit perplexed by the question in the boolean assessment that asks to identify which logic circuit best represents the given truth table. The Z term is left out of the logic circuit completely so I’m trying to figure out how to identify which logic gate just represents the X Y terms independent of Z.

You said that z is out of the logic circuit but why does it exist in the table!

the answer is the first figure :white_check_mark:
Here is how you check the first figure:
not gate :
This gate reverses so when 0 is passed through it it becomes 1 and 1 becomes 0.
so look at x in the table its conditions are 0 0 0 0 1 1 1 1 when these conditions pass through not gate they become 1 1 1 1 0 0 0 0
…Now we have
x after passing through not gate that became 1 1 1 1 0 0 0 0
y that hasn’t passed through any gate until now so its conditions still 0 0 1 1 0 0 1 1

now there is only And gate
And gate:
This gate returns 1 if all conditions are 1 if one condition is 0 it returns 0

so when x after reversing and y pass through it as there in the figure
that will produce 0 0 1 1 0 0 0 0

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