3. (30 pts) Express the following problems as languages, and then show that they are undecidable using map reduction and the known undecidable problem ATM (a) HelloWorldTM: determine whether a given TM halts on the input string "Hello" and loops on the input string "World" (b) PALINDROMETM: determine whether a given TM rejects all palindromes over the alphabet 0, 1, a, b 3. (30 pts) Express the following problems as languages, and then show that they are undecidable using map reduction and the known undecidable problem ATM (a) HelloWorldTM: determine whether a given TM halts on the input string "Hello" and loops on the input string "World" (b) PALINDROMETM: determine whether a given TM rejects all palindromes over the alphabet 0, 1, a, b