Use symbols to write the logical form of these arguments. If the argument is val
ID: 3885197 • Letter: U
Question
Use symbols to write the logical form of these arguments. If the argument is valid, identify the rule of inference that guarantees its validity. Otherwise, state whether the converse or the inverse error is made:
a
If at least one of these two numbers is divisible by 6, then the product of these two numbers is divisible by 6.
Neither of these two numbers is divisible by 6.
The product of these two numbers is not divisible by 6.
b
If I get a Christmas bonus, I’ll buy a stereo.
If I sell my motorcycle, I’ll buy a stereo.
If I get a Christmas bonus or I sell my motorcycle, then I’ll buy a stereo.
Use symbols to write the logical form of these arguments. If the argument is valid, identify the rule of inference that guarantees its validity. Otherwise, state whether the converse or the inverse error is made:
a
If at least one of these two numbers is divisible by 6, then the product of these two numbers is divisible by 6.
Neither of these two numbers is divisible by 6.
The product of these two numbers is not divisible by 6.
b
If I get a Christmas bonus, I’ll buy a stereo.
If I sell my motorcycle, I’ll buy a stereo.
If I get a Christmas bonus or I sell my motorcycle, then I’ll buy a stereo.
Explanation / Answer
A)
p : At least one of the two numbers is divisible by 6.
p' : None of the two numbers is divisible by 6.
Q : product of two numbers is divisible by 6.
Now, it is given that p -> Q is true and p' is also true and p is false.
Now further argument is made that Q' is also true.
Here the given argument is invalid.
p -> Q is true and p is false, so truth value of Q can be true or false both.
Hence Q can be true or false but argument is made that Q is false from given statements , Hence the argument is not necessarily true.
So we can say that argument is invalid.
Now , if Q -> p was true and p is false then we can say that Q is also false.
So inverse error is made here as Q->p is inverse of p->Q
B)
p : I get a christmas bonus.
q : i'll buy stereo.
r : i sell my motorcycle.
here p -> q and r -> q is true.
argument is made that (p v r) -> q .
which is valid argument.
Here when p->q and r->q is given.
if p or r any of them is true then q is also true.
hence if (pvr) is true then q is also true.
So we can say that given argument is valid.
if you have any doubts then you can ask in comment section.
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