Let `a:~(p ^^ ~r) vv (~ q vv s ) and b:(p vv s ) lar (q ^^ r)`. If the truth values of p and q are true and that of r and s are false, then the truth values of a and b are respectively . . .

Options

A. F,F
B. T,T
C. T,F
D. F,T

Answer

A

Explanation

Given, `p,q to T` and `r,stoF`
`thereforea:~(p ^^ ~ r) vv (~ q vv s)-= ~ (T ^^ T) vv (F vv )`
`-=~(T)vv (F)-=F vv F-=F`
and `b:(p vv s )larr (q ^^ r)`
`-=(~(p vv s) vv (q ^^ r)) ^^ (( p vv s) vv ~ (q ^^ r))`
`because p larr q -=(~ p vv q) ^^ (p vv ~ q)`
`-=(~(T vv F) vv (T ^^ F)) ^^ ((T vv F) vv ~ (T ^^ F))`
`-=(F vv F) ^^ (T vv T)`
`-=F ^^ T -=F`