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1-10. It can be proved (see Exercises 1-95 and 3-40) that every logical function can be represented with the operations A. V. - Therefore, as long as enough AND-gates, OR-gates and inverters are available, any logical function can be encoded on a chip. However, because of the way transistors behave, the easiest logical gate to put on a chip is a "NAND"="NOT AND" gate, A NAND gate returns a value of O (FALSE) iff both entries are set to I (TRUE), hence the name. The corresponding operation in logic is ple, where the connective "T" is also called the Sheffer stroke. (a) Prove that -p can be represented by using only the Sheffer stroke. (b) Prove that p q can be represented by using only the Sheffer stroke. (c) Prove that p q can be represented by using only the Sheffer stroke. (d) Conclude that any logical function can be represented by using only the Sheffer stroke. Hint. You may assume that the answer in Exercise 1-9b is affirmative