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d. 
qquad 
+(-21)=5
Diagonals are not allowed.
3. Verify the following properties for each of the given values of 
a,b and 
c.
2. A player who completes the 
f
Property 
1:a÷(b+c)!=(a÷b)+c box and writes down the give paper. The player also gets as
Property 2: 
a ×(b+c)=(a × b)+(a × c)
Property 3: 
a ×(b-c)=(a × b)-(a × c)
3. The game ends when no mor
2. 
F
3. 
a=-1,b=11 and 
c=2
b. 
a=-3,b=1 and 
c=-4
4. 'To calculate each player's 
s a.

d. \qquad +(21)=5 +(-21)=5 \newlineDiagonals are not allowed.\newline33. Verify the following properties for each of the given values of a,b a, b and c c .\newline22. A player who completes the f \mathrm{f} \newlineProperty 1:a÷(b+c)(a÷b)+c 1: a \div(b+c) \neq(a \div b)+c box and writes down the give paper. The player also gets as\newlineProperty 22: a×(b+c)=(a×b)+(a×c) a \times(b+c)=(a \times b)+(a \times c) \newlineProperty 33: a×(bc)=(a×b)(a×c) a \times(b-c)=(a \times b)-(a \times c) \newline33. The game ends when no mor\newline22. F \mathrm{F} \newline33. a=1,b=11 a=-1, b=11 and +(21)=5 +(-21)=5 00\newlineb. +(21)=5 +(-21)=5 11 and +(21)=5 +(-21)=5 22\newline44. 'To calculate each player's +(21)=5 +(-21)=5 33 a.

Full solution

Q. d. \qquad +(21)=5 +(-21)=5 \newlineDiagonals are not allowed.\newline33. Verify the following properties for each of the given values of a,b a, b and c c .\newline22. A player who completes the f \mathrm{f} \newlineProperty 1:a÷(b+c)(a÷b)+c 1: a \div(b+c) \neq(a \div b)+c box and writes down the give paper. The player also gets as\newlineProperty 22: a×(b+c)=(a×b)+(a×c) a \times(b+c)=(a \times b)+(a \times c) \newlineProperty 33: a×(bc)=(a×b)(a×c) a \times(b-c)=(a \times b)-(a \times c) \newline33. The game ends when no mor\newline22. F \mathrm{F} \newline33. a=1,b=11 a=-1, b=11 and +(21)=5 +(-21)=5 00\newlineb. +(21)=5 +(-21)=5 11 and +(21)=5 +(-21)=5 22\newline44. 'To calculate each player's +(21)=5 +(-21)=5 33 a.
  1. Isolate and Solve for d: To find the value of dd, we need to isolate dd on one side of the equation.d+(21)=5d + (-21) = 5d21=5d - 21 = 5Now, add 2121 to both sides to solve for dd.d21+21=5+21d - 21 + 21 = 5 + 21d=26d = 26
  2. Verify Property 11: Now let's verify Property 11 for a=1a = -1, b=11b = 11, and c=2c = 2.\newlineProperty 11 states that a÷(b+c)(a÷b)+ca \div (b + c) \neq (a \div b) + c.\newlineFirst, calculate the left side of the property.\newlinea÷(b+c)=1÷(11+2)=1÷13a \div (b + c) = -1 \div (11 + 2) = -1 \div 13\newlineNow, calculate the right side of the property.\newline(a÷b)+c=(1÷11)+2=111+2(a \div b) + c = (-1 \div 11) + 2 = -\frac{1}{11} + 2\newlineSince 113111+2-\frac{1}{13} \neq -\frac{1}{11} + 2, Property 11 holds.
  3. Verify Property 22: Next, verify Property 22 for a=1a = -1, b=11b = 11, and c=2c = 2. Property 22 states that a×(b+c)=(a×b)+(a×c)a \times (b + c) = (a \times b) + (a \times c). First, calculate the left side of the property. a×(b+c)=1×(11+2)=1×13=13a \times (b + c) = -1 \times (11 + 2) = -1 \times 13 = -13 Now, calculate the right side of the property. (a×b)+(a×c)=(1×11)+(1×2)=112=13(a \times b) + (a \times c) = (-1 \times 11) + (-1 \times 2) = -11 - 2 = -13 Since 13=13-13 = -13, Property 22 holds.
  4. Verify Property 33: Finally, verify Property 33 for a=1a = -1, b=11b = 11, and c=2c = 2. Property 33 states that a×(bc)=(a×b)(a×c)a \times (b - c) = (a \times b) - (a \times c). First, calculate the left side of the property. a×(bc)=1×(112)=1×9=9a \times (b - c) = -1 \times (11 - 2) = -1 \times 9 = -9 Now, calculate the right side of the property. (a×b)(a×c)=(1×11)(1×2)=11+2=9(a \times b) - (a \times c) = (-1 \times 11) - (-1 \times 2) = -11 + 2 = -9 Since 9=9-9 = -9, Property 33 holds.

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