(4) i (5) s (6) .. a is b (c) 12. Suppose that the following propositions have been proven: (1)~q→ r, and (2) if r. then either ~p or q. Give a paragraph proof of the proposition p q. it has been established that p implies either r or s, and

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Chapter2: Second-order Linear Odes
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Please anwser question 12(2.1)

Definition a .
Axiom 1: r4
Theorem 1: If a is e then q t.
Theorem 2:1 s
is said to be b iffr-
Elt in the missing reasons in the two-column proof that follows:
Theorem: If a is e then a is b.
Proof
Given: a is C
Prove: a is b (i.e.., r s)
CONCLUSIONS
JUSTIFICATIONS
(1) a is c
(2) r
(3) q
(4)t
(5) s
(6) .. a is b
Given
Assumption for r s
Axiom 1
(a)
(b)
(c)
12. Suppose that the following propositions have been proven: (1) ~q → r, and (2) if
r. then either~p or q. Give a paragraph proof of the proposition p q.
13. Suppose it has been established that p implies either r or s, and
Theorem 1: y → ~p
Theorem 2: r → x
Theorem 3: s → y
Theorem 4: x q
Prove, in outline form, that p → q.
GROUP C
the following have been established or assumed:
Transcribed Image Text:Definition a . Axiom 1: r4 Theorem 1: If a is e then q t. Theorem 2:1 s is said to be b iffr- Elt in the missing reasons in the two-column proof that follows: Theorem: If a is e then a is b. Proof Given: a is C Prove: a is b (i.e.., r s) CONCLUSIONS JUSTIFICATIONS (1) a is c (2) r (3) q (4)t (5) s (6) .. a is b Given Assumption for r s Axiom 1 (a) (b) (c) 12. Suppose that the following propositions have been proven: (1) ~q → r, and (2) if r. then either~p or q. Give a paragraph proof of the proposition p q. 13. Suppose it has been established that p implies either r or s, and Theorem 1: y → ~p Theorem 2: r → x Theorem 3: s → y Theorem 4: x q Prove, in outline form, that p → q. GROUP C the following have been established or assumed:
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