a) Each of the following statements in Boolean Algebra is true; explain why in each case the statement is true using your addition and times tables from above. There are two possible inputs for A since it can only take on the values of 0 or 1. i) A+0=A ii) A+1=1 iii) A+ A = A v) Ax1= A iv) A+A=1 (A is the complement of A) iii) A+ (AxB) = A+B vi) Ax

Question

a) Each of the following statements in Boolean Algebra is true; explain why in each case the statement is true using your addition and times tables from above. There are two possible inputs for A since it can only take on the values of 0 or 1. i) A+0=A ii) A+1=1 iii) A+ A = A v) Ax1= A iv) A+A=1 (A is the complement of A) iii) A+ (AxB) = A+B vi) AxA=A b) Each of the following statements in Boolean Algebra is true; explain why in each case the statement is true. Since each input for A and/or B can only take on the values of 0 and 1 there are four possible inputs for the compound statements. i) A+ (AxB) = A ii) (A+B)+(A x B) = A + B

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a) Each of the following statements in Boolean Algebra is true; explain why in each case the statement is true using your addition and times tables from above. There are two possible inputs for A since it can only take on the values of 0 or 1 . i)

A + 0 = A

ii)

A + 1 = 1

iii)

A + A = A

iv)

A + \overset{ˉ}{A} = 1

(

\overset{ˉ}{A}

is the complement of

A

) v)

A \times 1 = A

vi)

A \times A = A

b) Each of the following statements in Boolean Algebra is true; explain why in each case the statement is true. Since each input for A and/or B can only take on the values of 0 and 1 there are four possible inputs for the compound statements. i)

A + (A \times B) = A

ii)

(A + B) + (A \times B) = A + B

iii)

A + (\overset{ˉ}{A} \times B) = A + B

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