A predicate is ____________________. The truth set of a predicate P(x) with doma
ID: 3028520 • Letter: A
Question
A predicate is ____________________.
The truth set of a predicate P(x) with domain D is ____________________.
A statement of the form “x D, Q(x)” is true if, and only if, ____________________.
A statement of the form “x D, Q(x)" is true if, and only if, ____________________.
A universal conditional statement is a statement of the form ____________________.
A negation of a universal statement is an ____________________statement.
A negation of an existential statement is a ____________________statement.
A statement of the form “All A are B" can be written with a quantifier and a variable as
____________________.
A statement of the form “Some A are B" can be written with a quantifier and a variable as
____________________.
A statement of the form “No A are B" can be written with a quantifier and a variable as
____________________.
A negation for a statement of the form “x D, Q(x)" is ____________________.
A negation for a statement of the form “x D such that Q(x)" is ____________________.
A negation for a statement of the form “x D, if P(x) then Q(x)" is
____________________.
In general, a statement of the form “x D, if P(x) then Q(x)" is called vacuously true if, and
only if, _____________________,
Given a statement of the form “x, if P(x) then Q(x),"
the contrapositive is ____________________,
the converse is ____________________,
and the inverse is ____________________.
If you want to establish the truth of a statement of the form
“x D, y E such that P(x, y),"
your challenge is to allow someone else to pick ____________________, and then you must
find ____________________ for which P(x, y) ____________________.
If you want to establish the truth of a statement of the form
“x D such that y E, P(x, y),"
your job is to find ____________________ with the property that no matter what
____________________, P(x, y) will be ____________________.
A negation for a statement of the form “x D, y E such that P(x, y)" is
____________________.
A negation for a statement of the form “x D such that y E, P(x, y)" is
____________________.
Explanation / Answer
ANSWER :-
A predicate is a sentence that contains a nite number of variables and becomes a statement when specic values are substituted for the variables.
The truth set of a predicate P(x) with domain D is true when they are substituted for x.The truth set P(x) is denoted by {x D|P(x)}.
A statement of the form “x D, Q(x)” is true if, and only if,Q(x) is true for every x in D.
A statement of the form “x D, Q(x)" is true if, and only if, Q(x) is true for at least one x in D.
A universal conditional statement is a statement of the form x, if P(x) then Q(x).
The negation of a statement of the formx D , Q(x) is logically equivalent to a statement of form
x D,~ Q(x):
~(x D, Q(x)) = x D,~ Q(x)
The negation of a statement of the form x D, Q(x), is logically equivalent to the statement of form x D ,~ Q(x)
~(x D, Q(x)) = x D, ~ Q(x)
A negation for a statement of the form “x D, Q(x)" is logically equivalent to the statement x D, ~Q(x)
A negation for a statement of the form “x D such that Q(x)" is is logically equivalent to of form x D ,~ Q(x).
In general, a statement of the form “x D, if P(x) then Q(x)" is called vacuously true if, and only if P(x) is false for every x in D .
Given a statement of the form “x, if P(x) then Q(x),
the contrapositive is x D, if Q(x) then P(x)
the converse is x D, if Q(x) then P(x)
and the inverse is x D, if P(x) then Q(x).
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