For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of ( (98 Θ 33) Θ 17 )− ( 98 Θ (33 Θ 17) ) ?a)-10b)-2c)8d)13Correct answer is option 'D'. Can you explain this answer?

Question

For all positive integers m and v, the expression m &Theta; v represents the remainder when m is divided by v. What is the value of ( (98 &Theta; 33) &Theta; 17 )&minus; ( 98 &Theta; (33 &Theta; 17) ) ?a)-10b)-2c)8d)13Correct answer is option 'D'. Can you explain this answer?

Answer

First for ((98 Θ 33) Θ 17), determine 98 Θ 33, which equalsd to 32, since 32 is remainder when 98 divided with 33 ( 98 = 2(33) + 32 ).

Then determine 32 Θ 17 which equals to 15, since 15 is the remainder when 32 is divided by 17( 33= 1(17) +15)

Thus ( (98 Θ 33) Θ 17 ) = 15

Next, for (98 Θ (33 Θ 17)) , determine 33 Θ 17, which equalsd to 16, since16is remainder when33 divided with17 ( 33 = 1(17) + 16 ).

Then determine 98 Θ 16 which equals to 2, since 2 is the remainder when 98 is divided by 16 ( 98 = 6(16) + 2)

Thus (98 Θ (33 Θ 17)) = 2

Finally ((98 Θ 33) Θ 17)− (98 Θ (33 Θ 17)) = 15 - 2 = 13

Answer

First for ((98 Θ 33) Θ 17), determine 98 Θ 33, which equalsd to 32, since 32 is remainder when 98 divided with 33 ( 98 = 2(33) + 32 ).

Then determine 32 Θ 17 which equals to 15, since 15 is the remainder when 32 is divided by 17( 33= 1(17) +15)

Thus ( (98 Θ 33) Θ 17 ) = 15

Next, for (98 Θ (33 Θ 17)) , determine 33 Θ 17, which equalsd to 16, since16is remainder when33 divided with17 ( 33 = 1(17) + 16 ).

Then determine 98 Θ 16 which equals to 2, since 2 is the remainder when 98 is divided by 16 ( 98 = 6(16) + 2)

Thus (98 Θ (33 Θ 17)) = 2

Finally ((98 Θ 33) Θ 17)− (98 Θ (33 Θ 17)) = 15 - 2 = 13

Answer

First for ((98 Θ 33) Θ 17), determine 98 Θ 33, which equalsd to 32, since 32 is remainder when 98 divided with 33 ( 98 = 2(33) + 32 ).

Then determine 32 Θ 17 which equals to 15, since 15 is the remainder when 32 is divided by 17( 33= 1(17) +15)

Thus ( (98 Θ 33) Θ 17 ) = 15

Next, for (98 Θ (33 Θ 17)) , determine 33 Θ 17, which equalsd to 16, since16is remainder when33 divided with17 ( 33 = 1(17) + 16 ).

Then determine 98 Θ 16 which equals to 2, since 2 is the remainder when 98 is divided by 16 ( 98 = 6(16) + 2)

Thus (98 Θ (33 Θ 17)) = 2

Finally ((98 Θ 33) Θ 17)− (98 Θ (33 Θ 17)) = 15 - 2 = 13

Answer

Understanding the Problem
We need to evaluate the expression:
( (98 Θ 33) Θ 17 ) - ( 98 Θ (33 Θ 17) )
where m Θ v represents the remainder when m is divided by v.
Step 1: Calculate 98 Θ 33
- 98 divided by 33 gives a quotient of 2 (since 33*2=66).
- The remainder is 98 - 66 = 32.
So, 98 Θ 33 = 32.
Step 2: Calculate (98 Θ 33) Θ 17
- We now find 32 Θ 17.
- 32 divided by 17 gives a quotient of 1 (since 17*1=17).
- The remainder is 32 - 17 = 15.
So, (98 Θ 33) Θ 17 = 15.
Step 3: Calculate 33 Θ 17
- 33 divided by 17 gives a quotient of 1 (since 17*1=17).
- The remainder is 33 - 17 = 16.
So, 33 Θ 17 = 16.
Step 4: Calculate 98 Θ (33 Θ 17)
- Now we find 98 Θ 16.
- 98 divided by 16 gives a quotient of 6 (since 16*6=96).
- The remainder is 98 - 96 = 2.
So, 98 Θ (33 Θ 17) = 2.
Step 5: Final Calculation
We now combine our results:
( (98 Θ 33) Θ 17 ) - ( 98 Θ (33 Θ 17) ) = 15 - 2 = 13.
Final Result
Thus, the value of the expression is 13, which corresponds to option 'D'.

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