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Which of the following is correct?

  1. $(01)^* \cap (10)^* = \phi$
  2. $(a + b + c)^* = a^*b^*c^* + a^*b^* + c^* + c^*a^*b^*$
  3. $(p + q)^* p + (p + q)^* q + \epsilon = (p^* q^*)^*$
  4. $( y + z)^*  \cap (y + z)^* yz   \neq ( y + z)^* yz$
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A. False, $\epsilon$ is common in both $(01)^*$ and $(10)^*$

B. False, LHS contain strings as $abab, ababab$ etc RHS doesn't.

C.True, $(p+q)^*p+(p+q)^*q+\epsilon =$ strings over $\{p,q\}$ those ends with $p$     $+$ those ends with $q$    $ +$ those doesnt end with p or q (i.e, $\epsilon$) = all strings over $\{p,q\}$ , i.e,$ (p+q)^* = (p^*q^*)^*$

D.False , all strings over $\{y,z\}$ (that also includes all strings ending with $yz$ ) $\bigcap$ all strings $\{y,z\}$ ending with $yz= (y+z)^*yz$
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