(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
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28a88382-6ec1-4393-ac86-3b4f05a3e53a%2F984ebaee-2c99-4a7d-8927-b953567b2444%2Fhj6qj3_processed.jpeg&w=3840&q=75)
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