Mathematics
Use deductive reasoning to answer the following:
(i) Humans are mammals. All mammals are vertebrates. Based on these two statements, what can you conclude about humans?
(ii) Anthony is a barber. Dinesh had his hair cut. Can you conclude that Antony cut Dinesh’s hair?
(iii) Martians have red tongues. Gulag is a Martian. Based on these two statements, what can you conclude about Gulag?
(iv) If it rains for more than four hours on a particular day, the gutters will have to be cleaned the next day. It has rained for 6 hours today. What can we conclude about the condition of the gutters tomorrow?
(v) What is the fallacy in the cow’s reasoning in the cartoon below?
Answer
(i) Since, all humans are mammals and all mammals are vertebrates.
∴ We can conclude that,
Humans are vertebrates.
(ii) Since, Anthony is a barber and Dinesh had his hair cut.
∴ We can conclude that,
It is not necessary that Antony has cut Dinesh’s hair, as Dinesh could have got his hair cut by another barber.
(iii) Since, Martians have red tongues and Gulag is a Martian.
∴ We can conclude that,
Gulag has a red tongue.
(iv) Given,
If it rains for more than four hours on a particular day, the gutters will have to be cleaned the next day and it has rained for 6 hours today.
∴ We can conclude that,
The gutters will have to be cleaned tomorrow.
(v) We know that,
All animals have tails need not be dogs. For example, animals such as buffaloes, monkeys, cats, etc. have tails but are not dogs.
Related Questions
State whether the following statements are true or false. Give reasons for your answers.
(i) The sum of the interior angles of a quadrilateral is 350°.
(ii) For any real number x, x2 ≥ 0.
(iii) A rhombus is a parallelogram.
(iv) The sum of two even numbers is even.
(v) The sum of two odd numbers is odd.
Restate the following statements with appropriate conditions, so that they become true statements.
(i) All prime numbers are odd.
(ii) Two times a real number is always even.
(iii) For any x, 3x + 1 > 4.
(iv) For any x, x3 ≥ 0.
(v) In every triangle, a median is also an angle bisector.
Once again you are given four cards. Each card has a number printed on one side and a letter on the other side. Which are the only two cards you need to turn over to check whether the following rule holds?
"If a card has a consonant on one side, then it has an odd number on the other side."
Take any three consecutive even numbers and find their product; for example, 2 × 4 × 6 = 48, 4 × 6 × 8 = 192, and so on. Make three conjectures about these products.