Question

1. Proveif ?∈?,then1+(−1)!(2?−1)is a multiple of four

2. If?={∅,{∅}}, which of the following statements is true:

a.∅⊆?

b.{∅}⊆?

c.{∅}∈?

3. Provide a grammar for all bit strings that start with exactly one zero followed by even number of 1’s.

Answer 1

2) If?={∅,{∅}}

a) ∅⊆? --- True

Explanation : ∅ is the subset of every set .

b) {∅} ⊆ ? --- True

Explanation :

This statement means the set {∅} is a subset of the set containing element ∅ & set {∅}. The set {∅} contains only the element ∅ . Since  ∅ is also an element in {∅,{∅}} , the statement becomes true .

c) {∅}∈? --- True

Explanation :

3) Grammar for all bit strings that start with exactly one zero followed by even number of 1’s.

S ---> 0A

A ---> 1A1 | 11 | ε

For Question No. 1 either there is some writing mistake please comment below the right information .

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