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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+5gt7if and only if 4+6lt10. |
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Answer» SOLUTION :(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]` |
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