Give the lambda term that needs to replace \(\alpha\) so that the reduction results as given.

1. @@math_item

   content=\(\alpha \cnct a \cnct b = b \cnct a\)@@

2. @@math_item

   content=\(\alpha \cnct a \cnct b \cnct c = a \cnct c \cnct b\)@@

3. @@math_item

   content=\(\alpha \cnct a \cnct b \cnct c = a \cnct (c \cnct b)\)@@

4. @@math_item

   content=\(\alpha \cnct a \cnct b = \lambda x.a \cnct x \cnct (b \cnct x)\)@@

5. @@math_item

   content=\(\alpha \cnct (\lambda x.a \cnct x)c = ac\)@@

6. @@math_item

   content=\(\alpha \cnct (\lambda x.a \cnct x)c = \lambda y.a(yc)\)@@

7. @@math_item

   content=\(\alpha \cnct (\lambda x.sleeps'x) = sleeps'john'\)@@

8. @@math_item

   content=\(\alpha \cnct sleeps' = sleeps'john'\)@@

9. @@math_item

   content=\(\alpha (\lambda x. walks'x) john' \equiv_{\beta} slow'(walks'john')\)@@

10. @@math_item

    content=\(\alpha (\lambda x. walks'x) john' \equiv_{\beta} slow'walks'john'\)@@

11. @@math_item

    content=\(\alpha\cnct{mary'}john'(\lambda x.walks'x) \equiv_{\beta} walks'john' \land walks'mary'\)@@

12. @@math_item

    content=\(\alpha(\lambda x. talks'x)(\lambda x.smiles'x)john'\equiv_{\beta} smiles'john' \land talks'john'\)@@