Question 1
EXERCISE A1.5
- 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.
- For a conditional statement of the form "If , then ":
- Hypothesis (): The condition following "If".
- Conclusion (): The result following "then".
- The converse is formed by swapping the hypothesis and conclusion, resulting in "If , then ".
(i) If it is hot in Tokyo, then Sharan sweats a lot.
(i) If Sharan sweats a lot, then it is hot in Tokyo.
(ii) If Shalini is hungry, then her stomach grumbles.
(ii) If Shalini's stomach grumbles, then she is hungry.
(iii) If Jaswant has a scholarship, then she can get a degree.
(iii) If Jaswant can get a degree, then she has a scholarship.
(iv) If a plant has flowers, then it is alive.
(iv) If a plant is alive, then it has flowers.
(v) If an animal is a cat, then it has a tail.
(v) If an animal has a tail, then it is a cat.
- Confusing Converse with Inverse/Negation: The converse only swaps and ("If , then "). Do not negate the statements (e.g. writing "If it is not hot...").
- Assuming the Converse is True: A statement and its converse do not necessarily have the same truth value (for example, a living plant doesn't necessarily have flowers).
More questions in A1.5
EXERCISE A1.5
- 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.
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 , then .
(iv) If ABCD is a parallelogram, then AC and BD bisect each other.
(v) If , , and are whole numbers, then .
(vi) If and are two odd numbers, then is an even number.
(vii) If vertices of a parallelogram lie on a circle, then it is a rectangle.