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ddd [48]
3 years ago
13

A conditional statement is logically equivalent to a biconditional statement. True False pls help i have a test and i was absent

for 3 days i know nothing about this help help help help pls
Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
3 0

Answer:

false.

Step-by-step explanation:

A conditional statement is something like:

If P, then Q.

This means that if a given proposition P is true, then another proposition Q is also true.

An example of this is:

P = its raining

Q = there are clouds in the sky.

So the conditional statement is

If its raining, then there are clouds in the sky.

A biconditional statement is:

P if and only if Q.

This means that P is only true if Q is true, and Q is only true if P is true.

So, using the previous propositions we get:

Its raining if and only if there are clouds in the sky.

This statement is false, because is possible to have clouds in the sky and not rain.

(this statement implies that if there are clouds in the sky, there should be rain)

Then we could see that for the same propositions, the conditional statement is true and the biconditional statement is false.

Then these statements are not logically equivalent.

The statement is false.

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Lets denote c the concatenation of strings. For a binary string <em>a</em> in B9, we define the element f(a) in E10 this way:

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Step-by-step explanation:

To show that the function f defined above is a bijective function, we need to prove that f is well defined, injective and surjective.

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To see this, we need to show that f sends elements fromo b9 to elements of E10. first note that f(a) has 1 more binary integer than a, thus, it has 10. if a has an even number of 1's, then f(a) also has an even number because a 0 was added. On the other hand, if a has an odd number of 1's, then f(a) has one more 1, as a consecuence it will have an even number of 1's. This shows that, independently of the case, f(a) is an element of E10. Thus, f is well defined.

f is injective (or one on one):

If a and b are 2 different binary strings, then f(a) and f(b) will also be different because the first 9 elements of f(a) form a and the first elements of f(b) form b, thus f(a) is different from f(b). This proves that f in injective.

f is surjective:

Let y be an element of E10, Let x be the first 9 elements of y, then f(x) = y:

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This shows that f is well defined from B9 to E10, injective, and surjective, thus it is a bijection.

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