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”
The Answer to the Question
is below this banner.
Can't find a solution anywhere?
NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?
Get the Answers Now!You will get a detailed answer to your question or assignment in the shortest time possible.
Here's the Solution to this Question
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