Fundamental Boolean Laws Quiz

The Identity Law states that for any Boolean variable A, A OR 0 equals A. This is because 0 is the identity element for the OR operation, meaning that ORing any variable with 0 leaves the variable unchanged. Similarly, A AND 1 = A is also an example of the Identity Law for the AND operation.

The Domination Law states that for any Boolean variable A, A OR 1 equals 1. This is because 1 dominates the OR operation; if one operand is 1, the result is always 1, regardless of the other operand. Similarly, A AND 0 = 0 is also an example of the Domination Law for the AND operation.

The Identity Law states that for any Boolean variable A, A AND 1 equals A. This is because 1 is the identity element for the AND operation, meaning that ANDing any variable with 1 leaves the variable unchanged. Similarly, A OR 0 = A is also an example of the Identity Law for the OR operation.

The Domination Law states that for any Boolean variable A, A AND 0 equals 0. This is because 0 dominates the AND operation; if one operand is 0, the result is always 0, regardless of the other operand. Similarly, A OR 1 = 1 is also an example of the Domination Law for the OR operation.

The Idempotent Law states that for any Boolean variable A, A OR A equals A. This means that ORing a variable with itself does not change its value. Similarly, A AND A = A is also an example of the Idempotent Law for the AND operation.

The Idempotent Law states that for any Boolean variable A, A AND A equals A. This means that ANDing a variable with itself does not change its value. Similarly, A OR A = A is also an example of the Idempotent Law for the OR operation.

The Complement Law states that for any Boolean variable A, A OR NOT A equals 1. This is because either A or its negation must be true, so their OR is always true, represented by 1. Similarly, A AND NOT A = 0 is also an example of the Complement Law.

The Complement Law states that for any Boolean variable A, A AND NOT A equals 0. This is because A and its negation cannot both be true simultaneously, so their AND is always false, represented by 0. Similarly, A OR NOT A = 1 is also an example of the Complement Law.

The Involution Law states that for any Boolean variable A, NOT NOT A equals A. This means that double negation cancels out, and the original variable is obtained. It is also known as the double negation law.

The commutativity law for OR states that the order of operands does not affect the result of the OR operation. Thus, A OR B is equivalent to B OR A. This is similar to the commutativity of addition in arithmetic.

The commutativity law for AND states that the order of operands does not affect the result of the AND operation. Thus, A AND B is equivalent to B AND A. This is similar to the commutativity of multiplication in arithmetic.

The associativity law for OR states that when multiple OR operations are performed, the grouping of variables does not affect the result. Thus, (A OR B) OR C is equivalent to A OR (B OR C). This allows writing expressions like A OR B OR C without parentheses.

The associativity law for AND states that when multiple AND operations are performed, the grouping of variables does not affect the result. Thus, (A AND B) AND C is equivalent to A AND (B AND C). This allows writing expressions like A AND B AND C without parentheses.

The distributive law of AND over OR states that AND can be distributed over OR in a similar way to multiplication over addition in arithmetic. Thus, A AND (B OR C) equals (A AND B) OR (A AND C). This means that A is ANDed with each term inside the parentheses.

Boolean expressions are formed by combining Boolean variables using logical operators such as AND, OR, and NOT. These operators evaluate to true or false values, unlike arithmetic operators that perform numerical operations, relational operators that compare values, or assignment operators that assign values.