Exercises 1. Which of the following sentences are propositions? For those that are, indicate value. a. 123 is a prime number. b. 0 is an even number. c. \( x^{2}-4=0 \). d. Multiply \( 5 x+2 \) by 3 . e. What an impossible question! 2. State the negation of each of the following statements. a. \( \sqrt{2} \) is a rational number. b. 0 is not a negative integer. c. 111 is a prime number.

10. Найти собственные значения и собственные и присоединенные векторы матрицы лнейного оператора и найти вид этой матрицы в базисе пз собственных и присоединенных векторов \[ \left[\begin{array}{rrr}5 & 4 & -4 \\ -1 & 3 & 1 \\ 0 & 2 & 2\end{array}\right] \]

11. Write any three objectives of teaching Mathematics at Primary level, 12. What is the Socio-Cultural background of mathematical knowledge? 13. Give three merits of Play-Way method. 14. Draw the Indian place value chart and represent the number 58308 . 15. Add \( 2.342,3.04 \) and 8.2 . 16. Divide 0.245 by 6 . 17. Define Scalene triangle, Isosceles triangle and Equilateral triangle. 18. What do you mean by comprehensiveness of evaluation? 19. Mention any three purposes of evaluation. 20. Give a list of three tools and three techniques of evaluation in Mathematics.

(g) Let \( M=\left(\begin{array}{ccc}-4 & -4 & 4 \\ -1 & 0 & 1 \\ -7 & -6 & 7\end{array}\right) \). 4 Given that \( I \) is the \( 3 \times 3 \) identity matrix, determine the values of the copstant \( \lambda \) so that \( M+\lambda I \) is singular.

Determining the number of people who are accountable to a single manager refers to A. Chain of command B. Degree of ecentralization C. Span of control D. Degree of specialization

20. Show that \( \sqrt{3} \) is an irrational number. 21. Show that \( ((p \Rightarrow q) \wedge(q \Rightarrow r)) \Rightarrow(p \Rightarrow r) \) is tautology or not. (2 pts) 22. Show that \( p \Rightarrow(q \vee r) \) and \( (p \Rightarrow q) \vee(p \Rightarrow r) \) are equivalent. ( 2 pts)