Answer to Question #309661 in Discrete Mathematics for Huang

Question

Let P (x) be the statement "x can speak Russian" and let

Q(x) be the statement "x knows the computer language

C++." Express each of these sentences in terms of P (x),

Q (x), quantifiers, and logical connectives. The domain

for quantifiers consists of all students at your school.

Answer 1

Answer

Let P (x) be the statement "x can speak Russian" and let Q(x) be the statement "x knows the computer language C++." Express each of these sentences in terms of P (x), Q (x), quantifiers, and logical connectives. The domain for quantifiers consists of all students at your school.

$P(x)$ means "$x$ can speak Russian Language"

$Q(x)$ means "$x$ knows the computer language C++"

Now there can be a person who knows Russian Language and also knows the computer language C++.

So we can write this sentence in terms of P (x), Q (x), quantifiers, and logical connectives as

$\exist x(P(x)∧Q(x))$

Here $\exist$ is existential quantifier

And $∧$ is logical connective.