1. The problem involves evaluating the truth of statements about sets, numbers, algebraic expressions, and solving linear equations. 2. For the true/false section: - A set is a well-defined group of objects called elements that share common characteristics. This is true. - An empty set has no elements. This is true. - Union is the set of all elements in A and B; intersection is the set of elements common to both A and B, not elements in A but not in B. So the statement is false. - Natural numbers usually start from 1, but if zero is included, it is denoted by \( \mathbb{N}_0 = \{0,1,2,3,\ldots\} \). The statement says natural numbers contain zero and are denoted by \( \mathbb{N} \), which is false if \( \mathbb{N} \) excludes zero. - The universal set \( U \) contains all objects under consideration. True. - All natural numbers are not whole numbers is false because whole numbers include natural numbers and zero. - Integers include whole numbers and their negatives. True. - Negative integers are to the left of zero and less than zero. True. - Every negative integer is greater than positive integer is false. - A term without a variable is a constant term; all constant terms are like terms. True. 3. Fill in the blanks: 11. Monomial 12. Equation 13. Linear equation 14. Parallel 15. Parallel 16. x-axis 17. y-axis 18. Coordinates 4. Multiple choice: 19. Solve \(5x + 6 = 1\): \[5x = 1 - 6 = -5 \implies x = \frac{-5}{5} = -1\] Answer: A 20. Solve \(\frac{2a}{3} - 10 = 12\): \[\frac{2a}{3} = 22 \implies 2a = 66 \implies a = 33\] Answer: B 21. Sum \(7 + (-12) + (-3 + 6) = 7 - 12 + 3 = -2\) Answer: B 22. Check true statements: - 5 - 12 = -7 (not 17) - 7 - 7 = 0 (not 14) - 1 - (-1) = 2 (true) - -8/-8 = 1 (not -1) Answer: C 23. Calculate \(\frac{4}{7} + \frac{3}{7} - \left(\frac{1}{2} + \frac{3}{2}\right) = \frac{7}{7} - 2 = 1 - 2 = -1\) Answer: D 24. Calculate \(\frac{1}{2} + \frac{7}{5} + \frac{4}{5} = \frac{1}{2} + \frac{11}{5} = \frac{5}{10} + \frac{22}{10} = \frac{27}{10} = 2.7\) Final answers: 1. True 2. True 3. False 4. False 5. True 6. False 7. True 8. True 9. False 10. True 11. Monomial 12. Equation 13. Linear equation 14. Parallel 15. Parallel 16. x-axis 17. y-axis 18. Coordinates 19. A 20. B 21. B 22. C 23. D 24. 27/10