Answer to Question #194352 in Discrete Mathematics for Hassam

Question

Determine the truth-values of the followings

“ 1+1=4 if and only if earth is round”

“ Milk is white if and only if birds lay eggs”

“ Sky is white if and only if 1=0”

“ 33 is divisible by 5 if and only if hours has four legs”

“ x > 5 if and only if x2 > 25” 

Answer 1

The truth table for biconditional statement is-

i) " 1+1=4 if and only if earth is round"

let first statement p =1+1=4 and q= earth is round

Truth table for biconditional statement

p is false(F) statement and also q is false(F) statement

so truth value of i ) statement is true (T)

ii ) " Milk is white if and only if birds lay eggs"

p = Milk is white, which is true (T) statement

q = birds lay eggs, which is true (T) statement

truth value of ii) statement is true (T)

iii) " Sky is white if and only if 1=0"

p=Sky is white , which is false (F) statement

q=1=0, which is false (F) statement

So truth value of iii) statement is true (T)

iv) " 33 is divisible by 5 if and only if horse has four legs "

p = 33 is divisible by 5, which is false (F) statement

q= horse has four legs , which is true (T) statement

So truth value of iv) statement is false (F)

v) "x>5 if and only if x²>25"

This is not a statement so we can not determined their truth value