Prove or disprove that the following inference rules for functional dependencies. A proof can be made by using inference rules IR1 through IR3. A disproof should be done by showing a relational instance that refutes the conditions and functional dependencies in the left hand side of the inference rule but do not satisfy the conditions or dependencies in the right hand side:

a) {W->Y, X->Z} |= {WX->Y}
b) {X->Y} andImage for Question: Prove or disprove the following inference rules for functional dependencies. A proof can be made eit|= {X->Z}

c) {X->Y, X->W, WY->Z} |= {X->Z}

d) {XY->Z, Y->W} |= {XW->Z}

e) {X->Z, Y->Z} |= {X->Y}

f) {X->Y, XY->Z} |= {X->Z}

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For this assignment you have to write a c program that will take an infix expression as input and display the postfix expression of the input. after converting to the postfix expression, the program should evaluate the expression from the postfix and display the result. what should you submit? write all the code in a single file and upload the .c file. compliance with rules: ucf golden rules apply towards this assignment and submission. assignment rules mentioned in syllabus, are also applied in this submission. the ta and instructor can call any students for explaining any part of the code in order to better assess your authorship and for further clarification if needed. problem: we as humans write math expression in infix notation, e. g. 5 + 2 (the operators are written in-between the operands). in computer's language, however, it is preferred to have the operators on the right side of the operands, ie. 5 2 +. for more complex expressions that include parenthesis and multiple operators, a compiler has to convert the expression into postfix first and then evaluate the resulting postfix write a program that takes an "infix" expression as input, uses stacks to convert it into postfix expression, and finally evaluates it. it must support the following operations: + - / * ^ % ( example infix expression: (7-3)/(2+2) postfix expression: 7 3 2 2 result: rubric: 1) if code does not compile in eustis server: 0. 2) checking the balance of the parenthesis: 2 points 3) incorrect postfix expression per test case: -2 points 4) correct postfix but incorrect evaluation per test case: -i points 5) handling single digit inputs: maximum 11 points 6) handling two-digit inputs: 100 percent (if pass all test cases)