I\'m supposed to prove it this way! a + b === some expression using only IF, a,

Question

I'm supposed to prove it this way!

a + b === some expression using only IF, a, b, T, F
a * b === some expression using only IF, a, b, T, F
~a === some expression using only IF, a, T, F

3. (5 points.)The logical futn IF, a, cts something if-statenn a programming language. It takes three arguments, p, a, and b, each of which y be T or F. It returns either T or F. It is defined by the following identities 1rF.cr, b) = b Prove that IF is functionally complete, all by itself. This is not described in Rosen

Explanation / Answer

Basically, you want to prove And Or and Not operations using this so which can be done as below

a+b will be IF(A, T, B) here if a is true then the output is true else it depends on B

A*B will be IF(A, B, F) i.e if A is false then the output is false else it depends on B

~A will be IF(A, F, T) i.e. if A is True then output is False else the output is True

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