Required information
Express the given sentence in terms of P(x), Q(x), quantifiers, and logical connectives.
Click and drag the appropriate word, symbol, or phrase into the most appropriate blank.
Let P(x) be the statement \"x can speak Russian\" and let Q(x) be the statement \"x knows the computer language C++.\"
Consider the statement, \"No student at your school either can speak Russian or knows C++.\" This statement is equivalent to
the statement
The statement is a(n)
statement, because of the word, \"All.\"
We
So, the appropriate quantifier to be applied at the beginning of the symbolic statement is
want this symbol to act on x, representing a student at your school. The phrase, \"do not\" indicates the inclusion of
symbol. The phrases, \"student at your school speaks Russian\" and \"student at your
the
school knows C++\" are directly symbolized by
respectively. Finally, the word \"or\" requires the
statement to employ the
Hence, the completed quantified statement is
$\forall x(P(x)Q(x))$
$\forall$
conjunction
P(x) and Q(x)
exclusive-or
exclusive-or
R(x) and C(x)
conditional
Some students speak
Russian or know C++.
Some students do not
speak Russian or know
C++.
disjunction
Q(x) and P(x)
existential
C(x) and R(x)
universal
All students do not
speak Russian or know
C++.
$\forall x(P(x)\lor \neg Q(x))$
$\forall x\neg(R(x)\lor C(x))$
$\forall x\neg(P(x)\lor Q(x))$
$\exists$
