Let S1, S2 and S3 be three sets defined as S1 = z[]C : |z - 1| [ ] [ 2 ] S2 = z[]C : Re((1…

Question

Let S1, S2 and S3 be three sets defined as

S1 = {z$$\in$$C : |z - 1| $$ \le $$ $$\sqrt 2 $$}

S2 = {z$$\in$$C : Re((1 - i)z) $$ \ge $$ 1}

S3 = {z$$\in$$C : Im(z) $$ \le $$ 1}

Then the set S1 $$\cap$$ S2 $$\cap$$ S3 :

Accepted Answer

Let, z = x + iy

S1 $$ \equiv $$ (x - 1)2 + y2 $$ \le $$ 2 ..... (1)

S2 $$ \equiv $$ x + y $$ \ge $$ 1 ..... (2)

S3 $$\equiv$$ y $$ \le $$ 1 .... (3)

$$ \Rightarrow $$ S1 $$\cap$$ S2 $$\cap$$ S3 has infinitely many elements.

Solutions · 1