Paper 4: Fundamentals of Business Mathematics & Statistic

1.46 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Arithmetic

(ii) If all sides of a triangle are not equal, then the triangle is not equilateral; If all sides of a triangle are

equal, then the triangle is equilateral.

(iii) If you are not entitled to get this job then you are not a graduate, If you are entitled to get this

job, then you are a graduate.

(iv) If the square of a number is not divisible by 4, then the number is not an even integer; If the square

of a number is divisible by 4, then the number is an even integer.

11. Find the truth value of each of the following statements :
    (i) If 7+6 = 13, then 14 – 9 =5. (ii) If 9 + 11 = 21, then 5 – 6 = –1. (iii) If 40 ÷ 5 = 9, then 5 – 13 4 (iv) If 3 + 7 =
    10, then 5 + 2 = 8.
    Ans. (i) True, (ii) True, (iii) True (iv) False


12. If p : “You are a science student”. Q : “y on study well” be two given simple statements, then express
    each of the following symbolic statement into sentences :
    (i) q ⇒ p (ii) p ⇒ q (iii) ~ p ⇒ ~ q (iv) ~ q ⇒ ~ p.
    Ans. (i) If you study well, then you a science student. (ii) If you are a science student then you study well (iii)
    If you are not a science student, then you do not study well (iv) If you do not study well, then you are not a
    science student.


13. Write the contrapositive and converse statements of ~ q ⇒ p.
    Ans. Contrapositive statement : ~ p ⇒ q ; converse statement : p ⇒ (~ q).


14. Write the contrapositive statement of the contrapositive statement of p ⇒ q.
    Ans. p ⇒ q.


15. Identify the Quantifiers from the following statements :
    (i) There exists a quadrilateral whose all sides are equal.
    (ii) For all real number x, x > 0.
    (iii) For at least one national number n, n∈A where A = {–1, 0, 3, 5}.
    Ans. (i) There exists (ii) For all (iii) For at least.


16. Using Quantifiers, express the following symbolic inequalities into statements :
    (i) N + 2 > 5, n ∈ N (ii) x^2 > 0, n ∈ R – {0}.
    Ans. (i) There exists a natural number n ∈ N such that n + 2 > 5.
    (ii) For every real number x ∈ R – {0}, x^2 > 0.


17. If x is real number and^3 =+ 0x5x then prove that x = 0 by contradiction process.