If Δ is an operation on integers such that aΔb=a−b−2, for all integers a,b . Then, 7Δ(−4)=

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answer is C.

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Detailed Solution

Given that, Δ is an operation.
a , b are the integers.
Now the operation on the integers a , b can be written as aΔb=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 7Δ(−4). It is similar to the operation on the integers a, b i.e. aΔb, where a=7, b=−4.
We will be substituting the above values in the given equation aΔb=a−b−2 to get the value of 7Δ(−4) .
⇒ We have aΔb=a−b−2
Substituting a=7, b=−4 in the above equation, then we will get
⇒7Δ(−4)=7−(−4)−2
We know that −(−a)=a or when we multiply a negative sign with the negative sign, we will get the positive sign, then we will get
7Δ(−4)=7+4−2
When we add 7 to 4 we will get 11 , then we will get
7Δ(−4)=11−2
When we subtract 2 from 11, then we will get 9
∴7Δ(−4)=9
Hence Option – 3 is the correct answer.

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