Translate the given statements in symbolic form and determine the truth value of each statement :
(1) 2 is a rational number and it is the only even prime number.
(2) `sqrt(3)` is a rational number or `3+ i` is a complex number.
(3) Neither 21 is a prime number nor it is divisible by 3.
(4) `3+5gt7` if and only if `4+6lt10`.

Explanation

(1) Let p: `sqrt5` is an irrational number.
q: `3+sqrt5` is a complex number.
Then the symolic form of the given statement is `p^^q`.
The truth value of p and q are T and F respectively.
`:.` the truth value of `p^^q` is F.
(2) Let p: Two triangles have equal areas.
q: They are similar.
Then the symbolic form of the given statement is `ptoq`.
If the truth values of p is T, then the truth value of q is F.
`:.` the truth value of `ptoq` is F. ........ `[TtoF-=]`
(3) Let p: `-2lt-1`.
q: i is a real number.
Then the symbolic form of the given statement is `p""iffq`
The truth values of of p and q are T and F respectively.
`:.` the truth value of `p""iffq` is F.
(4) `EEninN` such that `n+5gt10` is a true statement because any `ngt6` satisfies `n+5gt10`.
Hence, the truth value of the given statement is T.
(5) Let p: `AAninN,n^(2)+n` is an even number.
q: `AAninN,n^(2)-n` is an odd number.
Then the symbolic form of the given statement is `p^^q`.
The truth value of p and q are T and F respectively.
`:.` the truth value of `p^^q` is F. " ".....`[A^^F-=F]`