1. A farmer has a dog, a goat, and a cabbage. The goat can eat cabbage and the dog can eat the goat. However, the dog does not like the cabbage. The farmer has two barns, a north barn and a south barn. Let variables x, y, and z denote the position of the dog, goat, and cabbage in the south barn (0) or in the north barn (1), respectively. Let function F be an output that has a value of 1 if and only if anything in danger of being eaten. Write the truth table for the function.2. Let variable w denote the farmer position in the south (0) or the north side (1) barn. Nothing is in danger in the presence of the farmer. Now modify the truth table to include the effect of this variable on the function.
3. Give the canonical sum-of-products expression for the turth table of Problem 1.
4. Give the canoncical product-of-sums expression for the truth table of Problem 1.
5. Give the canonical sum-of-products expression for the turth table of Problem 2.
6. Give the canonical product-of-sums expression for the truth table of Problem 2.