FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 1.45Ans. (i) Two sides or two angles of an isosceles triangles are equal; true; Inclusive “or”
(ii) Two straight lines in a plane interest or parallel; true; Exclusive “or”.
(iii) The root of the equation^2 =+− 06x5x is 2 or 3; true; Inclusive “or”
(iv) 5 is a rational number or an irrational number; true; Exclusive “or”.
- Using the connecting word “if then” write the compound statement and its truth value:
(i) A number is divisible by 15. It is divisible by 3.
(ii) A quadrilateral is a rhombus. Its all sides are equal.
(iii) Jhon is born in India. He is an Indian.
(iv) 256 is an even number. Its square root is an even integer.
Ans. (i) If a number is divible by 15, then the number is divisible by 3; true (ii) If a quadrilateral is a rhombus,
then its all sides are equal; true (iii) If Jhon is born in India, then he is an Indian; true (iv) If 256 is an even
number, then its square root is an even integer; true. - Using the connecting word “only if” form the compound statement.
(i) I will not go out. It rains
(ii) Rita will pass the examination. She reads well.
(iii) He succeeds in every sphere of life. He works hard.
(iv) A quadrilateral is a rectangle. The diagonals of the quadrilateral bisect each other.
Ans. (i) I will not go out only if it rains. (ii) Rita will pass the examination only if she reads well. (iii) He succeeds
in every sphere of life only if he works hard. (iv) A quadrilateral is a rectangle only if its diagonal bisect each
other. - Using the connective “if any only if” form the compound statement and write its truth value.
(i) Two triangles are equiangular. The corresponding sides of the triangles are proportional
(ii) A racer wins the race. He runs fast.
(iii) A number is divisible by 3. The sum of the digits of the number is not divisible by 3.
(iv) The birds have wings. The trees have wings.
Ans. (i) Two triangles are equiangular if and only if their corresponding sides are proportional; True (ii) A
racer wins the race if and only if he runs fast; True (iii) A number is divisible by 3 if and only if the sum of digits
is not divisible by 3; False (iv) The birds have wings if and only if the trees have wings; False. - Write the contrapositive and converse statements of the followings :
(i) If you drink milk, then you will be strong.
(ii) If a triangle is equilateral, then its all sides are equal.
(iii) If you are a graduate, then you are entitled to get this job.
(iv) If a number is an even integer, then its square is divisible by 4.
Ans. (i) If you are not strong, then you do not drink milk; If you are strong, then you drink milk.