Mathematics
Write the converses of the following statements.
(i) If it is hot in Tokyo, then Sharan sweats a lot.
(ii) If Shalini is hungry, then her stomach grumbles.
(iii) If Jaswant has a scholarship, then she can get a degree.
(iv) If a plant has flowers, then it is alive.
(v) If an animal is a cat, then it has a tail.
Related Questions
In each of the following questions, there are two statements. State if the second is the negation of the first or not.
(i) Mumtaz is hungry ; Mumtaz is not hungry.
(ii) Some cats are black ; Some cats are brown.
(iii) All elephants are huge ; One elephant is not huge.
(iv) All fire engines are red ; All fire engines are not red.
(v) No man is a cow ; Some men are cows.
Write the converses of the following statements. Also, decide in each case whether the converse is true or false.
(i) If triangle ABC is isosceles, then its base angles are equal.
(ii) If an integer is odd, then its square is an odd integer.
(iii) If x2 = 1, then x = 1.
(iv) If ABCD is a parallelogram, then AC and BD bisect each other.
(v) If a, b and c, are whole numbers, then a + (b + c) = (a + b) + c.
(vi) If x and y are two odd numbers, then x + y is an even number.
(vii) If vertices of a parallelogram lie on a circle, then it is a rectangle.
Suppose a + b = c + d, and a < c. Use proof by contradiction to show b > d.