In Boolean (binary) multiplication, which of the following equalities is not true? Choose the statement that violates the AND-operation rules.

Introduction / Context:
In Boolean algebra, multiplication corresponds to the logical AND operation. Knowing the basic truth rules for AND is essential for analyzing logic circuits, simplifying expressions, and validating gate-level designs. This question asks you to spot the statement that contradicts the AND truth table.

Given Data / Assumptions:

• Boolean variables take values 0 (false) or 1 (true).
• Multiplication (·) represents AND.
• We compare simple two-operand cases.

Concept / Approach:
The AND truth table is: 0·0=0, 0·1=0, 1·0=0, 1·1=1. The operation outputs 1 only when both inputs are 1. Therefore, any statement asserting 0·1=1 or 1·0=1 is false. All other canonical combinations follow the rules above.

Step-by-Step Solution:
List the four possible operand pairs for AND: (0,0), (0,1), (1,0), (1,1).Apply AND rule: output is 1 iff both inputs are 1.Evaluate each given equality and compare with the rule.Identify the violation: “0 x 1 = 1.”

Verification / Alternative check:
Gate-level view: an AND gate requires both inputs high to drive its output high; with one input at 0, the output is forced low. This physical intuition matches the algebraic rule.

Why Other Options Are Wrong:
0·0=0, 1·0=0, and 1·1=1 are all correct AND identities. “None of the above” is wrong because there is a clearly incorrect statement present.

Common Pitfalls:
Confusing Boolean multiplication (AND) with arithmetic multiplication; in arithmetic, 0×1=0 too, but the conceptual grounding here is logical truth, not numeric magnitude.

Final Answer:
0 x 1 = 1