In a domain of natural numbers, use $P(x)$ for $x$ is prime and $Q(x)$ for $x$ is even. Also the symbols $ \ <,>$ for $x$ and $=$ for $y$ can be used.
Then write the following sentences into quantified statements.
(i) Some primes are even.
(ii) All even numbers are greater than $ 1 $ .
Answer:
I tried to write as follows:
(i) 'some primes are even' can be written as $ \exists <,> (\wedge Q(x)) $
Am I right ? Any help ?
Existential quantification is restricted by conjunction.
"Some A-things are B-things," means "There exists something which is an A-thing and is a B-thing." $$\exists x~\big(A(x)\wedge B(x)\big)$$
Universal quantification is restricted by implication (conditional).
"All A-things are B-things," means "Take anything, if it is an A-thing, then it is a B-thing." $$\forall x~\big(A(x)\to B(x)\big)$$