00:01
In this question, we are given a set a as a, b, c and t.
00:07
And we are given a composition table for addition operation.
00:13
The table is given as shown in this figure.
00:17
Now, we need to obtain a similar composition table for subtraction.
00:25
That is, we need to obtain an inverse composition table of the given.
00:30
Table.
00:32
Now let us first write what we obtain from the given table.
00:36
Firstly, a plus a is equal to a, a plus b is equal to b, a plus c is equal to c and a plus d is equal to d.
00:50
Therefore, a is the additive identity of the given composition.
00:59
Also we have given that b plus d is equal to a and d plus b also is equal to a.
01:10
That means b is the inverse of d, that is b is equal to negative of d.
01:16
That is additive inverse.
01:18
Similarly, d is equal to negative of b...