Recall that, in the Hilbert proof system H, АЛВ is the replacement for the formula ¬(A → ¬B). Prove that if we introduce conjunction as above, it has the usual commutativity property; i.e. show FH (A^ B) + (B A A). Remark: It is sufficient to prove one implication in the 'if and only if formula above, since the other one is proved analogously, by reversing the roles of A and B.
Recall that, in the Hilbert proof system H, АЛВ is the replacement for the formula ¬(A → ¬B). Prove that if we introduce conjunction as above, it has the usual commutativity property; i.e. show FH (A^ B) + (B A A). Remark: It is sufficient to prove one implication in the 'if and only if formula above, since the other one is proved analogously, by reversing the roles of A and B.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Recall that, in the Hilbert proof system H,
AA B
is the replacement for the formula -(A → ¬B). Prove that if we introduce
conjunction as above, it has the usual commutativity property; i.e. show
FH (A^ B) + (B ^ A).
Remark: It is sufficient to prove one implication in the 'if and only if'
formula above, since the other one is proved analogously, by reversing the
roles of A and B.
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