4. Prove that for any formulae A and B and variable p, A[p := B] is...

Question

Question

4. Prove that for any formulae A and B and variable p, A[p := B] is a well-formed!) formula.

engineering Computer-Science

Answer 1

Answer #1

Answer ? Answer: criven that A, B be formulas and p is a variabie Hence A,B be formulas & p. is variabic , so it defines Pep)

Answer 2

Similar Homework Help Questions

Assume that p NAND q is logically equivalent to ¬(p ∧ q). Then, (a) prove that...

Assume that p NAND q is logically equivalent to ¬(p ∧ q). Then, (a) prove that {NAND} is functionally complete, i.e., any propositional formula is equivalent to one whose only connective is NAND. Now, (b) prove that any propositional formula is equivalent to one whose only connectives are XOR and AND, along with the constant TRUE. Prove these using a series of logical equivalences.
For any events A, B, C, and D = A∩B∩C prove the following equality: P(D^c) =...

For any events A, B, C, and D = A∩B∩C prove the following equality: P(D^c) = 1−P(A)·P(B | A)·P(C | A∩B)
1. Use the formula P(A) PABP(B) + P(AlBc)P(B") to prove that if P(AB) P (AlBc) then...

1. Use the formula P(A) PABP(B) + P(AlBc)P(B") to prove that if P(AB) P (AlBc) then A and B are independent. Then prove the converse (that if A and B are independent then P(AIB)- P(ABe). [Assume that P(B) > 0 and P(B) > 0.]

1. Consider two independent events, A and B, where 0< P(A) <1,0< P(B)< 1. Prove that...

1. Consider two independent events, A and B, where 0< P(A) <1,0< P(B)< 1. Prove that A and B' are independent as well.
3. Let a >0, and for any A E Rnxn, define Aa aA (a) Prove that for any induced matrix norm, K(Ao)...

3. Let a >0, and for any A E Rnxn, define Aa aA (a) Prove that for any induced matrix norm, K(Ao) (b) Write the formula for det(Aa) in terms of det(A). estimating well/ill-conditioning of matrices. n(A) . Hint: examine IAall and IAal directly. (c) Based on your result from (a) and (b), comment on whether the determinant is useful for 3. Let a >0, and for any A E Rnxn, define Aa aA (a) Prove that for any induced...
4. 5 pts] Prove that P(A n B | C) = PAI B n C)P(B |...

4. 5 pts] Prove that P(A n B | C) = PAI B n C)P(B | C).

Prove/ Disprove : If A and B are any two events, then it is always true...

Prove/ Disprove : If A and B are any two events, then it is always true that P (A ∪ B) ≤ P (A) + P (B)
Consider two independent events, A and B, where 0くP(A) < 1,0くP(8)く1. Prove that A' and B'...

Consider two independent events, A and B, where 0くP(A) < 1,0くP(8)く1. Prove that A' and B' are independent as well.
. Prove that sequence in Example 6.2.2 (i) on p.174 converges uniformly to r on any inteval [a, b]. Prove that the...

. Prove that sequence in Example 6.2.2 (i) on p.174 converges uniformly to r on any inteval [a, b]. Prove that the convergence cannot be uniform on [0, 0o) J() d tel argue thau Jn J Exercise 6.2.6. Assume fn → f on a set A. Theorem 6.2.6 is an example of a typical type of question which asks whether a trait possessed by each fn is inherited by the limit function. Provide an example to show that all of...

If Matrix A, r(A)=n, prove that r(AB)=r(B), for any B nxp, and show that for any...

If Matrix A, r(A)=n, prove that r(AB)=r(B), for any B nxp, and show that for any invertible mxm matrix P, there exists Q mxn with full rank such that A=PQ