Let S1, S2 and S3 be three sets defined asS1 = {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 :

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 :

has exactly three elements

is a singleton

has infinitely many elements

has exactly two elements

Solution

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