When the conditional statement p q needs to be proved, state what needs to be as
ID: 3108951 • Letter: W
Question
When the conditional statement p q needs to be proved, state what needs to be assumed and what needs to be shown to prove the statement
• using direct proof,
• using proof by contraposition,
• using proof by contradiction.
1. When a quantified statement ”xP(x) is true” has to be proved, how would you proceed? Explain.
2. When a quantified statement ”xP(x) is true” has to be proved, how would you proceed? Explain.
3. When a quantified statement ”xP(x) is false” has to be proved, how would you proceed? Explain.
4. When a quantified statement ”xP(x) is false” has to be proved, how would you proceed? Explain.
Explanation / Answer
>> Using direct method
we will consider p statement and then we will show q statement.
>>using proof by contraposition
we will consider that statement q is not true then we will show that p is also not trure.
>>using proof by contradiction
we will consider that q is not true and p is true then we will show that p is not true.
1.Suppose we have to prove that ”xP(x) is true” then first we will take a arbitrary x then we wiil prove our statement for this x.
2..Suppose we have to prove that ”xP(x)'' is true then we can prove our result by contradiction method .first assume that our result is not true for any x. then show a contradiction.
3.we will proof this type of result by contradiction method. we will consider that suppose there exist x s.t result is true then will show a contradiction ,then say that our assumption was wrong. so there does not exist any x for which result is true.
4. we will proceed same as 3.
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