Question

If $ \Delta $ is an operation on integers such that $ a\Delta b=a-b-2 $ , for all integers $ a $ , $ b $ . Then, $ 7\Delta \left( -4 \right)= $
A. $ 11 $
B. $ -9 $
C. $ 9 $
D. $ 1 $

Answer 1

Hint: In the problem we have given the operation between the two integers say $ a $ , $ b $ and the operation is given by $ a\Delta b=a-b-2 $ . Now we need to calculate the value of operation for the given integers $ 7 $ , $ -4 $ mathematically it can be written as $ 7\Delta \left( -4 \right) $ . The above operation is similar to the operation between $ a $ , $ b $ , so we will substitute $ a=7 $ , $ b=-4 $ in the operation $ a\Delta b $ which is equal to $ a-b-2 $ . Now we can write the obtained value as the $ 7\Delta \left( -4 \right) $ .

Complete step by step answer:
Given that,
 $ \Delta $ is an operation.
 $ a $ , $ b $ are the integers.
Now the operation on the integers $ a $ , $ b $ can be written as $ a\Delta b=a-b-2 $ .
In the problem they have asked to calculate the value of operator on integers $ 7 $ , $ -4 $ . It can be mathematically written as $ 7\Delta \left( -4 \right) $ . It is similar to the operation on the integers $ a $ , $ b $ i.e. $ a\Delta b $ , where $ a=7 $ , $ b=-4 $ .
We will be substituting the above values in the given equation $ a\Delta b=a-b-2 $ to get the value of $ 7\Delta \left( -4 \right) $ .
 $ \Rightarrow $ We have $ a\Delta b=a-b-2 $
Substituting $ a=7 $ , $ b=-4 $ in the above equation, then we will get
 $ \Rightarrow 7\Delta \left( -4 \right)=7-\left( -4 \right)-2 $
We know that $ -\left( -a \right)=a $ or when we multiply a negative sign with the negative sign, we will get the positive sign, then we will get
 $ 7\Delta \left( -4 \right)=7+4-2 $
When we add $ 7 $ to $ 4 $ we will get $ 11 $ , then we will get
 $ 7\Delta \left( -4 \right)=11-2 $
When we subtract $ 2 $ from $ 11 $ , then we will get $ 9 $
 $ \therefore 7\Delta \left( -4 \right)=9 $
Hence Option – C is the correct answer.

Note:
 Generally, the operator symbol $ \Delta $ is an equation or relation established between the two integers by using the arithmetic operators. To find the operator value on the given integers we need to apply the arithmetic operators in a given sequence. There is a possibility that students might miss to include the -2 term and they might get the answer as 7+4=11 and choose option A as the correct answer. So, do not miss any such terms and do the calculation correctly.