P(x,y) means "x + 2y = xy", where x and y are integers.
Determine the truth value of the statement.
(a) P(1,-1).
(b) P(0, 0).
(c) ∃y P(3, y).
(d) ∀x ∃y P(x, y).
(e) ∃x ∀y P(x, y).
(f) ∀y ∃x P(x, y).
(g) ∃y ∀x P(x, y).
(h) CS173 Discrete Mathematical Structures ¬CS173 Discrete Mathematical Structures ∀x CS173 Discrete Mathematical Structures ∃y CS173 Discrete Mathematical Structures ¬P(x, y).
Hello, captainjapan!
Your quantifiers didn't show up.
I'll have to make some guesses . . .
We have: .means "
", where
and
are integers.
Determine the truth value of the statements.
\;P(1,-1))
. . . True
We have: .\;P(0, 0))
. . . True
We have:\;\exists y\: P(3, y))
. . There exists. . . True
This says:\;\forall x\:\forall y\:P(x, y))
for all
[Find your own counterexample.]
There is an\;\exists x\:\exists y\:P(x, y))
[See parts (a) and (b).]
This says: for any\;\forall y\:\exists x\: P(x, y))
If, we have: .
... not an integer.
\;\exists y\:\forall x\:P(x, y))
This says: for any
If, we have: .
... not an integer.
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