Problem $11$: For the following true table, write the logic equation for the functions $C$ and $S,$ and draw the corresponding circuit

$\backslash$table$[[A,B,C,$S$],[0,0,1,0],[0,1,1,1],[1,0,0,1],[1,1,1,1]]$

Problem $12$: Using Boolean Algebra Reduce the following logic expressions

a$)F(a,b)=a^{\text{'}}{b}^{\text{'}}+a^{\text{'}}b+ab$

b$)F(a,b)=a^{\text{'}}{b}^{\text{'}}+a^{\text{'}}b+a{b}^{\text{'}}$

c$)F(a,b,c)=a^{\text{'}}{b}^{\text{'}}c+a^{\text{'}}bc+abc$

d$)F(a,b,c)=ab+a^{\text{'}}b{c}^{\text{'}}+ac+bc+abc$

e$)F(a,b,c,d)=a^{\text{'}}{b}^{\text{'}}{c}^{\text{'}}{d}^{\text{'}}+a{b}^{\text{'}}cd+ab{c}^{\text{'}}d+a^{\text{'}}bcd+abc{d}^{\text{'}}$

f$)F(a,b,c,d)=a^{\text{'}}{b}^{\text{'}}+b^{\text{'}}c{d}^{\text{'}}+a{c}^{\text{'}}d+a^{\text{'}}bd+ab{c}^{\text{'}}{d}^{\text{'}}$

Problem $13.$ Give the logic equations of the following circuits.