Boolean algebra is essentially based on

Given below are four logic gate symbols (figure). Those for $OR$,$NOR$ and $NAND$ are respectively:

You are given two circuits as shown in the figure. Show that circuit $(a)$ acts as an $OR$ gate while circuit $(b)$ acts as an $AND$ gate.

In the logic circuit shown in the figure,if inputs $A$ and $B$ are $0$ and $1$ respectively,the output at $Y$ is $x$. The value of $x$ is...........

The following diagram performs the logic function of:

The following figure shows a logic gate circuit with two inputs $A$ and $B$ and the output $Y.$ The voltage waveforms of $A, B$ and $Y$ are as given. The logic gate is