. The figure on the right shows the floor plan of a room. The
side of each unit square represents 0.5 m. Write down:
the floor area of the room;
b. the length of the wall cabinet;
the approximate area of the corner table top;
d. the width of the sofa set; and
e. the approximate area of the coffee table top.
Answers
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
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 below