Show that the class of languages recognisable by push-down automata (i.e., the class of context-free languages) is closed under union and concatenation but not under intersection. Describe a Turing...

Show that the class of languages recognisable by push-down automata (i.e.,

the class of context-free languages) is closed under union and concatenation

but not under intersection.

Describe a Turing machine that recognises the language of the strings w•w,

where w is a string over an alphabet {0, 1}.