9) Write each of the arguments below symbolically and then explain whether it is
ID: 3139020 • Letter: 9
Question
9) Write each of the arguments below symbolically and then explain whether it is valid or not. a) If it is hot outside, then I will go swimming. l will not go swimming .. It is not hot outside. If it is not hot outside or if it is raining, then I will not go swimming. It is not raining .. I will not go swimming b) c)I will go swimming if and only if it is hot outside. l will not go swimming .. It is not hot outside. This problem is similar to Examples 2-5 and to Exercises 1-9 in Section 2.3 of your SNHU MAT230 textbook.Explanation / Answer
a) Let p = it is hot outside; q= I will go swimming
if it is hot outside then I will go swimming is equivalent to : p => q
When I will not go swimming it means q = F (False)
Hence it is not hot outside. This is VALID as if q is false and p is false then p=> q is TRUE as per the truth table.
b) Let p = I will not go swimming
q= It is not hot ouside
r= it is raining
Thus, it it is not ht outside of it is raining, then I will not go swimming is:
( q v r) => p
It is not raining means r is False, so the conclusion I will not go swimming which means P is True;
This need not be valid as it also depends on the statement 'q' (i.e. it is not hot outside or not)
NOT VALID
c) I will go swimming be = p
It is hot outside = q
The stamtent says p <=> q or p iff q
It is given that I will not go swimming , which is P is false
Conclusion is it is not hot outside which is Q is False;
This is a valid argument since in an iff and only iff statement, if one statement is False (or true) then the other statemnt HAS to be false too (or true too) for argument to be valid;
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