a) Explain what the productions are in a grammar if the Backus−Naur form for productions is as follows:
b) Find a derivation tree for
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Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
- Eliminate all useless productions from the grammar S→aS/AB A→bA B→AA What language does this grammar generate?arrow_forwardConsider a language which uses the following set of characters: Prefix set: { a e i } Small set: { b c d} Large set: { B C D} Punctuation set: { x y } This language must follow the following rules: i. A series must start with a prefix character ii. A series must end with a punctuation characterarrow_forwardUsing the symbolization key given, translate each English-Language sentence into SL.M: Those beings are men in pajamasL: Those beings are lymers O: Those beings are orangutans 1) Those beings are not men in pajamas.2) Those beings are men in pajamas, or they are not.3) Those beings are either orangutans or lymers.4) Those beings are neither orangutans nor lymers.5) If those beings are lymers, then they are neither orangutans nor men in pajamas.6) Unless those beings are men in pajamas, they are either lymers or they are orangutans.arrow_forward
- The following are equivalent statements: (i) a∈R is constructible from Q (ii) (a,0) is constructible from Q×Q (iii) (a,a) is constructible from Q×Q (iv) (0,a) is constructible from Q×Q.arrow_forwardTranslate the following statements into idiomatic English where C ( x, y ) means that student x is enrolled in class y, where the domain of x consists of all students in this course (which includes Jane) and the domain of y consists of all classes being offered at your school. C ( Jane, CMPSC 121 ) ∃x C ( x, IST 242 ) ∀x ( C ( x, CMPSC 101 ) ∧ C ( x, IST 250 ) ) ∀x∀y∃z (( x ≠ y ) ∧ C ( x, z ) ∧ C ( y, z ) ) ∃x∃y∀z (( x ≠ y ) ∧ ( C ( x, z) ↔ C ( y, z ) ) )arrow_forwardCheck the following logical equivalences: (P ^ ¬R) ⟹Q ⟹ (P ^ ¬Q) ⟹ R Note: Through the conjunctiva normal form. And argued.arrow_forward
- Using only the Primitive Rules, prove the following double sequent: (A v B) → A ⊣⊢ B → Aarrow_forwardConstruct npda's that accept the following languages on Σ = {a, b, c} a) L = {a^n b^2n : n ≥ 0}. b) L = {wcw^R: w ∈ {a , b}*}.arrow_forwardImagine that num_orders and num_instock are particular values, such as might occur during execution of a computer program. Write negations for the following statements. (num_orders < 50 and num_instock > 300) or (50 <= num_orders < 75 and num_instock > 500)arrow_forward
- Can you find the derivitive of the followinarrow_forwardIs there an associative property of subtraction? That is, is it always true that a – (b – c) = (a – b) – c for all real numbers a, b, and c? If so, explain why. If it’s not always true, give a counterexample with specific numbers to illustrate that conclusion.arrow_forwardExamine whether the following statements are true or false:(i) { a, b } ⊄ { b, c, a }(ii) { a, e } ⊂ { x : x is a vowel in the English alphabet}(iii) { 1, 2, 3 } ⊂ { 1, 3, 5 }(iv) { a } ⊂ { a, b, c }(v) { a } ∈ { a, b, c }(vi) { x : x is an even natural number less than 6} ⊂ { x : x is a natural number which divides 36}arrow_forward
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