Discrete math question Im stuck on Rewrite the conditional c

Discrete math question I\'m stuck on.

Rewrite the conditional ((c > 5 && b == a) || c >= 5) in a simpler way using a truth table.

(truth table please :D)

update: This is the whole question in the book. I can\'t give anymore information on it beside that a truth table would be something like....   A | B | C

            T     T    T     with true and false filled out.

Solution

as given we have to find the truth table for given condition

we have conditional statemnet given by,

((c > 5 && b == a) || c >= 5)

so we can say that we have three different conditions

let we can sau that we have 3 conditional statement

let condition X = c > 5 menas A = true = T when c > 5 otherwise X = false = F

let condition Y = b== a menas B = true = T when b==a otherwise Y = false = F

let condition Z = c >= 5 menas C = true = T when c >= 5 otherwise Z = false = F

we can write our conditional statement as

W = ((c > 5 && b == a) || c >= 5) = ((X && Y) || Z)

so we can say that W = True = T when ((X && Y) || Z) = T otherwise W = F

so find the truth table as below

where,

X = c > 5

Y = b==a

Z = c >=5

W = ((c > 5 && b == a) || c >= 5) = ((X && Y) || Z)

as W = ((X && Y) || Z),

W = T when Z = T

W = T when (X && Y ) = T means when X = T and Y = T

W = F when Z = F and (X && Y ) = F means W = F when Z = F and (X = F or Y = F)