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We define $T$ as: $T(B) = (b_0,b_1,b_2,b_3)$ We use $D$ to represent the difference of $X$ and $Y$: $D = X \oplus Y$ Compute $T(D)$: $T(D) = (d_0,d_1,d_2,d_3)$ $= (x_0 \oplus y_0, x_1 \oplus y_1, x_2 \oplus y_2, x_3 \oplus y_3)$ $=(x_0,x_1,x_2,x_3) \oplus (y_0,y_1,y_2,y_3)$ which is by definition of $T$: $T(X) \oplus T(Y)$



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