A student wants to decide whether he will go home during upcoming mid semester recess by using

combinational logic. He will not go if his performance in the last mid$-$semester exam was bad,

unless his SPI $($Semester Performance Index$)$ in the previous semester was good or all his friends

are going home during the recess. He will, however, go home anyway if he does not have enough

money to pay his mess bill. Assign suitable Boolean variables and obtain the condition for his

going home in the minimal sum of products form as well as in the minimal product of sums form.

Implement the functions by $2$ input NAND gate only. Also realize it by $2$:$1$ MUX.