Rewrite the following statements so that the quantifier trails the rest of the sentence.
a. For any graph G, the total degree of G is even.
b. For any isosceles triangle T, the base angles of T are equal.
c. There exists a prime number p such that p is even.
d. There exists a continuous function f such that f is not differentiable.
(a)
Consider the statement,
'For any graph \(G\), the total degree of \(G\) is even'.
The objective is to write the statement such that the quantifier trials the rest of the sentence.
The above sentence can be rewritten in trailing quantifier as follows:
The total degree of \(G\) is even for any graph \(G\).
Hence, the statement in trailing quantifier as:
The total degree of \(G\) is even for any graph \(G\).
(b)
Consider the statement,
'For any isosceles triangle T, the base angles of T are equal'.
The objective is to write the statement such that the quantifier trials the rest of the sentence.
The above statement can be rewritten in trailing quantifier as follows:
The base angles of T are equal for any isosceles triangle T.
Hence, the statement in trailing quantifier as:
The base angles of T are equal for any isosceles triangle T.
(c)
Consider the statement,
'There exists a prime number \(p\) such that \(p\) is even'.
The objective is to write the statement such that the quantifier trials the rest of the sentence.
The above statement can be rewritten in trailing quantifier as follows:
\(P\) is even for some prime numbers \(p\).
Hence, the statement in trailing quantifier as:
\(P\) is even for some prime numbers \(p\).
(d)
Consider the statement,
'There exists a continuous function f such that f is not differentiable'.
The objective is to write the statement such that the quantifier trials the rest of the sentence.
The above statement can be rewritten in trailing quantifier as follows:
f is not differentiable for some continuous function f.
Hence, the statement in trailing quantifier as:
f is not differentiable for some continuous function f.