**What is Boolean Algebra?**

Boolean algebra, a method for applying and studying mathematical logic, was created by George Boolean, an English mathematician. He wrote “An investigation into the law of thought” in 1854. This book outlined a theory of logic that uses symbols rather than words. Boolean algebra is a more algebraic approach to the subject.

#### Questions on Boolean Algebra Mathematics with answers:

**Ques. **In Boolean Algebra, the zero element ‘0’

(a) Has two values

(b) Is unique

(c) As atleast two values

(d) None of these

Ans. (b)

**Ques.** Let B={*p, q, r, …..} *and let two binary operations be denoted by ‘‘ and ‘’ or ‘+’ or ‘.’, then

(a) 0’ = 0

(b) 0’ = 1

(c) 1’ = 1

(d) None of these

Ans. (b)

**Ques. **In Boolean Algebra, the unit element ‘1’

(a) Has two values

(b) Is unique

(c) Has atleast two values

(d) None of these

Ans. (b)

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**Ques. **In a Boolean Algebra *B*, for all *x* in *B*, *x* *x* =

(a) 0

(b) 1

(c) *x*

(d) None of these

Ans. (c)

**Ques. **In a Boolean Algebra *B*, for all *x* in *B*, *x* *x* =

(a) 0

(b) 1

(c) *x*

(d) None of these

Ans. (c)

**Ques. **Let B = {*p, q, r, …..} *and let two binary operations be denoted by ‘‘ and ‘’ or ‘+’ or ‘.’, then

(a) a a = 0

(b) a a = a

(c) a 1 = a

(d) None of these

Ans. (b)

**Ques. **In a Boolean Algebra *B*, for all *x* in *B*, *x* 1 =

(a) 0

(b) 1

(c) *x*

(d) None of these

Ans. (b)

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**Ques. **In a Boolean Algebra *B*, for all *x*, *y* in *B*, *x* (*x* *y*) =

(a) *y*

(b) *x
*(c) 1

(d) 0

Ans. (b)

**Ques. **Let B={*p, q, r, …..} *and let two binary operations be denoted by ‘‘ and ‘’ or ‘+’ or ‘.’, then

(a) a (a b) = a

(b) a (a b) = b

(c) a (a b) = a b

(d) None of these

Ans. (a)

**Ques. **In a Boolean Algebra *B*, for all *x*, *y* in *B*, x (*x* *y*) =

(a) *y*

(b) *x
*(c) 1

(d) 0

Ans. (b)

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**Ques. **In a Boolean Algebra *B*, for all *x* in B, (*x*’)’ =

(a) *x*’

(b) *x
*(c) 1

(d) 0

Ans. (b)

**Ques. **In a Boolean Algebra *B*, for all *x*, *y* in *B,*(*x* *y*)’ =

(a) *x*’ v *y*’

(b) *x*’ *y*’

(c) 1

(d) None of these

Ans. (b)

**Ques. **In a Boolean Algebra *B*, for all *x*, *y* in B, (*x* *y*)’ =

(a) x’ y’

(b) x’ y’

(c) 1

(d) None of these

Ans. (b)

**Ques. **In a Boolean Algebra *B*, for all *x* in *B*, 1’ =

(a) 0

(b) 1

(c) x 1

(d) None of these

Ans. (a)

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**Ques.** Dual of (x’ y’) = x y is

(a) (x’ y’) = x y

(b) (x’ y’) = x y

(c) (x’ y’)’ = x y

(d) None of these

Ans. (b)

**Ques.** Dual of x (y x) = x is

(a) x (y x) = x

(b) x (y x) = x

(c) (x y) A(x x) = x

(d) None of these

Ans. (a)