Question

Tyrone Shoelaces has invested a huge amount of money into the stock market and doesnât trust just anyone to give him buying and selling information. Before he will buy a certain stock, he must get input from three sources. His first source is Pain Webster, a famous stock broker. His second source is Meg A. Cash, a self-made millionaire in the stock market, and his third source is Madame LaZora, world-famous psychic. After several months of receiving advice from all three, he has come to the following conclusions:

a) Buy if Pain and Meg both say yes and the psychic says no.

b) Buy if the psychic says yes.

c) Donât buy otherwise.

Construct a truth table and find the minimized Boolean function to implement the logic telling Tyrone when to buy.

Answer 1

The truth table is :

Pain Meg Psych Buy

`$0$`
`$0$`
`$0$`
`$0$`

`$0$`
`$0$`
`$1$`
`$1$`

`$0$`
`$1$`
`$0$`
`$0$`

`$0$`
`$1$`
`$1$`
`$1$`

`$1$`
`$0$`
`$0$`
`$0$`

`$1$`
`$0$`
`$1$`
`$1$`

`$1$`
`$1$`
`$0$`
`$1$`

`$1$`
`$1$`
`$1$`
`$1$`

The Boolean function :

`$\text{F(Pain, \ Meg, \ Psych)}$` =
`$\overline {\text{PainMeg}}\text{Psych}+\overline{\text{Pain}}\text{MegPsych}+\text{Pain}\overline{\text{Meg}}\text{Psych}+\text{PainMeg}\overline{\text{Psych}}$`
`$+\text{PainMegPsych}$`

Meg and Psych

`$00$` 01
`$11$` 10

Pain 0 1 1

`$1$`
`$1$` 1
`$1$`

Therefore,

`$\text{F(Pain, \ Meg, \ Psych)}$` = Psych + PainMeg