1. State if the following are true or false. \( \begin{array}{ll}\text { a) } 102+55=55+102 & \text { b. } 23+(781+806) \neq(23+781)+806 \\ \text { c. } 12(4+17)=(12 \times 4)+17 & \text { d. } 9(10-7)=(9 \times 10)-(9 \times 7) \\ \text { e. } 90-(21-8)=(90-21)-8 & \text { f. } 38+0 \neq 38 \\ \text { g. } 23 \times 1=1 & \text { H. } 70 \div 0=0 \\ \text { l. } 1 \times 173=173 & \text { J. }-1 \div 0 \text { is undefined } \\ \text { le. } 0+909=909 & \end{array} \)

Let's evaluate each statement to determine whether it is **True** or **False**: ### a) \( 102 + 55 = 55 + 102 \) **True** *Explanation:* Addition is commutative, meaning the order of addends does not affect the sum. ### b) \( 23 + (781 + 806) \neq (23 + 781) + 806 \) **False** *Explanation:* \[ 23 + (781 + 806) = 23 + 1587 = 1610 \] \[ (23 + 781) + 806 = 804 + 806 = 1610 \] Both sides are equal, so the statement claiming they are not equal is false. ### c) \( 12(4 + 17) = (12 \times 4) + 17 \) **False** *Explanation:* \[ 12(4 + 17) = 12 \times 21 = 252 \] \[ (12 \times 4) + 17 = 48 + 17 = 65 \] 252 does not equal 65. ### d) \( 9(10 - 7) = (9 \times 10) - (9 \times 7) \) **True** *Explanation:* \[ 9(10 - 7) = 9 \times 3 = 27 \] \[ (9 \times 10) - (9 \times 7) = 90 - 63 = 27 \] Both sides are equal. ### e) \( 90 - (21 - 8) = (90 - 21) - 8 \) **False** *Explanation:* \[ 90 - (21 - 8) = 90 - 13 = 77 \] \[ (90 - 21) - 8 = 69 - 8 = 61 \] 77 does not equal 61. ### f) \( 38 + 0 \neq 38 \) **False** *Explanation:* Adding zero to a number does not change its value. \[ 38 + 0 = 38 \] Thus, the statement claiming they are not equal is false. ### g) \( 23 \times 1 = 1 \) **False** *Explanation:* \[ 23 \times 1 = 23 \neq 1 \] ### h) \( 70 \div 0 = 0 \) **False** *Explanation:* Division by zero is undefined in mathematics. ### i) \( 1 \times 173 = 173 \) **True** *Explanation:* Multiplying by one does not change the value. \[ 1 \times 173 = 173 \] ### j) \( -1 \div 0 \) is undefined **True** *Explanation:* Division by zero is undefined, regardless of the numerator. ### k) \( 0 + 909 = 909 \) **True** *Explanation:* Adding zero does not change the value. \[ 0 + 909 = 909 \] ### Summary: - **a)** True - **b)** False - **c)** False - **d)** True - **e)** False - **f)** False - **g)** False - **h)** False - **i)** True - **j)** True - **k)** True