Question

Write a negation for each statement:

1. All squares are rectangles
2. There exists a segment that has no midpoint

Answer 1

Answer for 1.
All rectangles are squares.
❌ false

Answer for 2.
All segments have one midpoint.
✅ true

Reason - if a statement is true, then its negation is false and if a statement is false, then its negation is true. So the first statement is true so we have a false reply. The second one was false so we gave a true statement.

Answer 2

1. There exists at least one square that is not a rectangle.

2. Every segment has a midpoint.

Explanation:

1.The given statement is: "All squares are rectangles". We have to find the negation of the statement. The statement that gives the negative meaning of the given statement is called the negation of the given statement. So the negation of the given statement is, "There exists at least one square that is not a rectangle".

2.Every segment has a midpoint.