a) Create an unambiguous grammar which generates basic mathematical expressions (using numbers and the four operators +, -, *, /). Without parentheses, parsing and mathematically evaluating expressions created by this string should give the result you'd get while following the order of operations. For now, you may abstract "number" as a single terminal, n. In the order of operations, * and / should be given precendence over + and -. Aside from that, evaluation should occur from left to right. So 8/4*2 would result in 4, not 1. 1+2*3 would be 7. 4+3*5-6/2*4 would be 4+15-6/2*4 = 4+15-3*4 = 4+15-12 = 19-12 = 7. For reference, here is a grammar which implements basic mathematical expressions but is ambiguous: S -> S+S | S-S | S*S | S/S | n Which could generate expressions such as: n+n*n n-n+n/n-n*n Where n would stand for some number (though each n may stand for a different number in this example). b) Next, make the "n" a non-terminal and allow it to produce any non-negative integer, including 0 but not numbers with unnecessary leading 0s. Again, make sure it's unambiguous. c) Finally, add in the ability for the grammar to produce balanced parentheses around terms in a way such that anything inside parentheses is evaluated first, in the way that parentheses are normally handled. d) Create a pushdown automaton (PDA) th at recognizes the language generated by the grammar from part c). Explain the answer please
