Q.The gate which produces high output, when its both inputs are high is –

An AND gate's truth table gives a high (1) output only when every input is high.

For a two-input logic gate with inputs A, B: the AND gate follows $Y = A\cdot B$, so $Y=1$ only when $A=1$ and $B=1$ (both inputs high); for any other input combination $Y=0$. The OR-family and NAND/NOR gates behave differently — a NAND gate is high for every combination except both-high, and a NO …

The three fundamental logic gates are AND, OR and NOT.

Logic gates are the building blocks of digital circuits. The three fundamental (basic) gates are:

• OR — output 1 if any input is 1 (logical addition, A+B),
• AND — output 1 only if all inputs are 1 (logical multiplication, A·B),
• NOT — inverts the input (Ā). …

Logic gates implement binary decision-making, so they form the core of every digital device, from calculators to computers to automated control systems.

Application

Logic gates (AND, OR, NOT, NAND, NOR, XOR) combine binary (0/1, HIGH/LOW) inputs according to Boolean rules. A practical example: in a digital calculator or computer, arithmetic and logical operations are built up entirely from networks of logic gates; another example is an automatic control circuit (e.g. a security/alarm system) that switches on an output only when a specific combination of input conditions ("sensor triggered" AND "system armed") is satisfied.

§ Honest curriculum note

…

The logic gate that gives a high output if any one (or more) input is high is the OR gate.

…