In which of the logic gate the following statement is true? "The output is high when either of the inputs is high but not if both inputs are high"

The given statement states that the output is high ($1$) when either of the inputs is high ($1$), but the output is low ($0$) if both inputs are high ($1$).

This corresponds to the following truth table:
$A = 0, B = 0 \Rightarrow Y = 0$
$A = 1, B = 0 \Rightarrow Y = 1$
$A = 0, B = 1 \Rightarrow Y = 1$
$A = 1, B = 1 \Rightarrow Y = 0$

This is the characteristic truth table of an Exclusive-OR (X-OR) gate.

Answer: X-OR