1. Given the basic identities of Boolean algebra, prove that: AB+BC+AC=AB+BC+ AC 2. Given the basic identities of Boolean algebra, prove that: ABC+BCD+BC+CD=B+ CD 3. Use only NAND gates to draw the circuit for the Boolean function, F=AC+BC. 4. Write the truth table and draw the logic circuit for the following Boolean function: F=AB+ C+D 5. Simplify the following Boolean function using K-map and draw the logic circuit for the simplified function: F=ABCD+ABCD+ABCD+ABCD