write this symbolic statement in words:
~P<-->~Q
Mind your p's and qu's?
Sra
yes, sorry those are supposed to be lower case.
Let
P=if ABC is a right-triangle at B
Q=AB²+BC²=AC²
The given symbolic statement
~P <-> ~Q
translates to
ABC is NOT a right-triangle at B
if and only if AB²+BC² ≠ AC²
or in two sentence form:
(if ABC is NOT a right-triangle at B then AB²+BC² ≠) AND (if AB²+BC² ≠ then ABC is NOT a right-triangle at B.)
As per question,
P is not true if and only if Q is not true.
The equivalent is P is true if and only if Q is true.
Using p and q below write the symbolic statement in words. Assume that p and q are true
P: the value of x is 4
Q: 3x+2=14
The symbolic statement ~P <--> ~Q can be translated into words as "Not P if and only if not Q."
To understand how to translate this symbolic statement, let's break it down:
1. ~ (Tilde): This symbol represents negation or "not." So, ~P means "not P" and ~Q means "not Q."
2. <--> (Double-headed arrow): This symbol represents "if and only if" or "iff." It means that the two statements on each side of the arrow have the same truth value. In this case, ~P <--> ~Q indicates that the truth value of ~P is the same as the truth value of ~Q.
Putting it together, ~P <--> ~Q in words is "Not P if and only if not Q." This implies that if P is false, then Q is also false, and if Q is false, then P is also false. It captures the idea that the truth values of P and Q are exactly opposite.