Using Truth Table prove each of the following:

a$)A+A^{\text{'}}=1$

b$)(A+B{)}^{\text{'}}=A^{\text{'}}{B}^{\text{'}}$

c$)(AB{)}^{\text{'}}=A^{\text{'}}+B^{\text{'}}$

d$)$ XX$\text{'}=0$

e$)x+1=1$