Question

Complete the table by finding the time.
Duration of time
S.No.
Start time
End time
1.
8:00 p.m.
11 hours and 57 minutes
2.
7:51 p.m.
11 hours and 12 minutes
3.
6:20 p.m.
7 hours and 6 minutes
4.
9:31 p.m.
3:22 a.m.
5.
5:56 a.m.
11 hours and 33 minutes
6.
8:07 a.m.
1:51 p.m.
102​

Answer 1

Answer:

Negation of "For every ...", "For all ...", "There exists ..."Sometimes we encounter phrases such as "for every," "for any," "for all" and "there exists" in mathematical statements.Example.Consider the statement "For all integers , either  is even or  is odd". Although the phrasing is a bit different, this is a statement of the form "If A, then B." We can reword this sentence as follows: "If  is any integer, then either  is even or  is odd."

How would we negate this statement? For this statement to be false, all we would need is to find a single integer which is not even and not odd. In other words, the negation is the statement "There exists an integer , so that  is not even and  is not odd."

In general, when negating a statement involving "for all," "for every", the phrase "for all" gets replaced with "there exists." Similarly, when negating a statement involving "there exists", the phrase "there exists" gets replaced with "for every" or "for all."p and (negation p or negation q) and q =The negation of p ∧ q asserts “it is not the case that p and q are both true”. Thus, ¬(p ∧ q) is true exactly when one or both of p and q is false, that is, when ¬p ∨ ¬q is true. Similarly, ¬(p ∨ q) can be seen to the same as ¬p ∧ ¬q. Our reasoning can be checked on the truth tables belowThe negation of p ∧ q asserts “it is not the case that p and q are both true”. Thus, ¬(p ∧ q) is true exactly when one or both of p and q is false, that is, when ¬p ∨ ¬q is true. Similarly, ¬(p ∨ q) can be seen to the same as ¬p ∧ ¬q. Our reasoning can be checked on the truth tables belowThe negation of p ∧ q asserts “it is not the case that p and q are both true”. Thus, ¬(p ∧ q) is true exactly wh