{
    "translations": {
        "en": {
            "fa1": "../../../AV/VisFormalLang/NFA/AutomataFiles/NFA2DFA2a.jff",
        
            "q0": {
                "type": "multiple",
                "description": "We would like to prove that function $\\textit{fact}$ does indeed compute the factorial function. ",
                "question": "What is the result of $fact(4)$",
                "answer": "24",
                "choices": ["4", "10", "14", "24"]
            },
            "q1": {
                "type": "multiple",
                "description": "$\\textbf {Theorem}$: Function $\\textit{fact}$ will terminate for any value of n.",
                "question": "What is the base case?",
                "answer": "fact will terminate for $n$ $\\leq$ $0$",
                "choices": ["$fact(0) = 0$", "$fact(n) = n^*fact(n-1)$", "fact will terminate for $n$ $\\leq$ $0$"]
            },
            "q2": {
                "type": "multiple",
                "description": "For $fact(n)$, $fact$ will make a recursive call for $fact(n-1)$.",
                "question": "Will $fact(n)$ terminate?",
                "answer": "Yes",
                "choices": ["Yes", "No"]
            },
            "q3": {
                "type": "multiple",
                "description": "For $fact(n)$, $fact$ will make a recursive call for $fact(n-1)$.",
                "question": "Why will $fact(n)$ make a recursive call for $fact(n-1)$",
                "answer": "Using the induction hypothesis $fact(n-1)$ will terminate",
                "choices": ["Using the induction hypothesis $fact(n-1)$ will terminate", "since n is decremented, it will reach zero"]
            },
            "q4": {
                "type": "multiple",
                "description": "As it was mentioned before, we would like to prove that function fact does indeed compute the factorial function.<br> There are two distinct steps to such proof. The first is to prove that the function always terminates. The second is to prove that the function returns the correct value.",
                "question": "What is the next step?",
                "answer": "We only proved the first part (termination) now we need to prove that fact returns the correct value.",
                "choices": ["We are done the proof, so fact indeed calculate the factorial", "We only proved the first part (termination) now we need to prove that fact returns the correct value."]
            },
            "q5": {
                "type": "multiple",
                "description": "$\\textbf {Theorem}$: Function fact does compute the factorial function for any value $n \\geq 0$",
                "question": "Can fact calculate factorial $n \\geq 12$?",
                "answer": "Yes",
                "choices": ["Yes", "No"]
            },
            "q6": {
                "type": "multiple",
                "description": "First, we need to prove the base case.",
                "question": "Which of the following is the correct base case?",
                "answer": "All of the above",
                "choices": ["at $n = 0$, $fact(0) = 1$", "at $n = 1$, $fact(1) = 1$", "All of the above"]
            },
            "q7": {
                "type": "select",
                "description": "How the induction hypothesis helps to prove that fact(n) provides the n!?",
                "question": "How the induction hypothesis helps to prove that fact(n) provides the n!?",
                "answer": ["$fact(n) = n * fact(n-1)$", "$fact(n-1) = (n-1)!$", "$fact(n) = n * (n-1)! = n!$"],
                "choices": ["$fact(n) = n * fact(n-1)$", "$fact(n-1) = (n-1)!$", "$fact(n) = n * (n-1)! = n!$"]
            }
        }
    }
}