1.44 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICSArithmetic
Ans. (i) No. truth value; not a mathematical statement (ii) False; mathematical statement (iii) True;
mathematical statement (iv) No truth value; not a mathematical statement (v) “True”; mathematical
statement (vi) No truth value; not a mathematical statement.- Write the negation of each of the following statements :
(i) Australia is a continent. (ii) The length of the sides of each parallelogram are equal. (iii) 3 is a
rational number. (iv) The difference between 12 and 28 is 14. (v) All rhombuses are parallelogram.
Ans. (i) Australia is not a continent or it is not true that Australia is a continent. (ii) The length of the sides of
each parallelogram are not equal or it is not true that the length of the sides of each parallelogram are
equal (iii) 3 is not a rational number or it is not true that 3 is a rational number. (iv) The difference
between 12 and 28 is not 14 or it is not true that the difference between 12 and 28 is 14. (v) All rhombuses are
not parallelogram or it is not ture that all rhombuses are parallelogram. - Identify the simple and compound mathematical statements. Write the components of compound
mathematical statements. Write the truth value in each case. (i) The diagonals of a parallelogram are
not equal (ii) x is a real number and 2x + 5 is a rational number (iii) 42 is an even integer and it is divisible
by 2, 3, 7. (iv) London is a big city it is the capital of England. (v) The moon is a star.
Ans. (i) Simle mathematical statement; true (ii) compound mathematical statement; x is a real number;
2x+5 is a rational number; false (iii) compound mathematical statement; 42 is an even integer, 42 is divisible
by 2, 42 is divisible by 3, 42 is divisible by 7 ; ture (iv) compound mathematical statement; London is a big
city, London is the capital of India; true. (v) mathematical statement; false. - Write the compound mathematical statement using the connective “and” and then write the truth
value :
(i) 7 is a prime number 7 is an odd integer.
(ii) The earth is a planet. The earth moves round the sun.
(iii) Vellor belongs to India. Vellor is the capital of Tamilnadu.
(iv) All integers are positive and negative; false.
Ans. (i) 7 is a prime number and it is an odd ingeter; true
(ii) The earth is a planet and it moves round the sun; true
(iii) Vellor belongs to India and it is the capital of Tamilnadu; false
(iv) All integers are positive and negative; false. - Using the connecting word “or” write the compound statement in each case and write the truth
value and the type or “or”.
(i) Two sides of an isosceles triangle are equal. Two angles of an isosceles triangle are equal.
(ii) Two straight lines in a plane intersect at a point. Two straight lines in a plane are parallel.
(iii) 2 is a root of the equation^2 =+− 06x5x. 3 is a root of the equation^2 =+− 06x5x.
(iv) 5 is a rational number. 5 is an irrational number.