Predicates P and Q are defined below. The domain of discourse is the set of all
ID: 3912519 • Letter: P
Question
Predicates P and Q are defined below. The domain of discourse is the set of all positive integers.
P(x): x is prime
Q(x): x is a perfect square (i.e., x = y2, for some integer y)
Find whether each logical expression is a proposition. If the expression is a proposition, then determine its truth value.
?x Q(x)
[ Choose ] Proposition. Truth value is FALSE. Proposition. Truth value is TRUE. Not a proposition.
?x Q(x) ? ¬P(x)
[ Choose ] Proposition. Truth value is FALSE. Proposition. Truth value is TRUE. Not a proposition.
?x Q(x) ? P(3)
[ Choose ] Proposition. Truth value is FALSE. Proposition. Truth value is TRUE. Not a proposition.
?x (Q(x) ? P(x))
[ Choose ] Proposition. Truth value is FALSE. Proposition. Truth value is TRUE. Not a proposition.
?x (¬Q(x) ? P(x))
Explanation / Answer
?x Q(x)
[ Choose ]
Proposition. Truth value is FALSE.
Proposition. Truth value is TRUE.
Not a proposition.
Answer:
Proposition. Truth value is TRUE.
explanation:
there exist a x where x is perfect square for a value y...
if we can find a value for x then the proposition is true...
let x=4..then y =2
Since we can find a value for x,
the proposition is true,,
?x Q(x) ? ¬P(x)
[ Choose ]
Proposition. Truth value is FALSE.
Proposition. Truth value is TRUE.
Not a proposition.
Answer:
Proposition. Truth value is False.
explanation:
proposition meaning: for all x ,x is a perfect square and x is not a prime
but for all values...x can't be a perfect square
if we can find a value for x where it is not a perfect square then it is false
x=5 is not perfect square
so... ?x Q(x) is false..
and is x is prime
so.. ¬P(x) it is also false
hence..false and false is false
?x Q(x) ? P(3)
[ Choose ]
Proposition. Truth value is FALSE.
Proposition. Truth value is TRUE.
Not a proposition.
Answer:
Proposition. Truth value is TRUE.
explanation:
proposition meaning: for all x ,x is a perfect square or 3 is a prime
but for all values...x can't be a perfect square
if we can find a value for x where it is not a perfect square then it is false
x=5 is not perfect square
so... ?x Q(x) is false..
and is 3 is prime
so.. P(3) it is true
hence..false or true is true
?x (Q(x) ? P(x))
[ Choose ]
Proposition. Truth value is FALSE.
Proposition. Truth value is TRUE.
Not a proposition.
Answer:
Proposition. Truth value is False.
explanation:
proposition meaning: there exist x where ,x is a perfect square and x is a prime
here if x is a perfect square then it cant be prime...
hence it is false
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