Basic Doubt in Rice Theorem

Question

I read this blog http://gatecse.in/rices-theorem/ and I have a doubt in the first property.

An example in this blog is L(M) = {0} and it's written that TM_no =sigma* . My doubt is how can it be sigma* as sigma* can also contain {0} which should be accepted by TM.

Comments

@Arjun Sir Please reply

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can contain and "=" are different. The proparty is "= {0}" and not "containing 0" meaning it restricts any other strings in L.

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L1 = {<M> | M is a TM and L(M) ⊆ {00, 11}}

L2 = {<M> | M is a TM and L(M) = {00, 11}}

Sir, according to me L2 should be RE but I am confused about L1? Can you please explain? I think that incase of L1 TM_yes and TM_no would be mutually exclusive.

@Arjun

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@Arjun sir, I had the same doubt as in question.

 TM_no =sigma*,is it because it is not containing only 0?

TM_no =sigma* and this is not same as L={0},as it contains extras strings apart from L.Is this correct understanding?

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@Xylene Both L1 and L2 are not r.e.

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@Rahul Yes, "0" is the reason for the first statement. Did not get your second query.

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Sir, for both the questions TMyes = {00,11} and TMno = {00,11,01} and TMyes is subset of TMno and hence both are not re right?

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yes, you are correct. I was thinking something else.