Mathematics
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.
Mathematics Proofs
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Answer
(i) This statement is false because the sum of the interior angles of a quadrilateral is 360°.
(ii) This statement is true for all real numbers (x), x2 ≥ 0.
(iii) This statement is true because in a rhombus, both pairs of opposite sides are parallel and hence every rhombus is a parallelogram.
(iv) This statement is true because this is true for any two even numbers.
(v) This statement is false because the sum of any two odd numbers is always an even number.
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Related Questions
State whether the following statements are always true, always false or ambiguous. Justify your answers.
(i) There are 13 months in a year.
(ii) Diwali falls on a Friday.
(iii) The temperature in Magadi is 26°C.
(iv) The earth has one moon.
(v) Dogs can fly.
(vi) February has only 28 days.
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.
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?
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."
