Question

In: Computer Science

Prove that the following two statements are not logically equivalent. In your proof, completely justify your...

Prove that the following two statements are not logically equivalent. In your proof, completely justify your answer.

(a) A real number is less than 1 only if its reciprocal is greater than 1.

(b) Having a reciprocal greater than 1 is a sufficient condition for a real number to be less than 1.

Proof:

 
 
 
#2. 
Prove that the following is a valid argument:

         All real numbers have nonnegative squares.

The number i has a negative square.

         Therefore, the number i is not a real number.

Proof:

Solutions

Expert Solution

SOLUTION-

For #2 : The conclusion is logically follows from the premises. So the given argument is valid

IF YOU HAVE ANY DOUBT PLEASE COMMENT DOWN BELOW I WILL SOLVE IT FOR YOU:)
----------------PLEASE RATE THE ANSWER-----------THANK YOU!!!!!!!!----------


Related Solutions

Prove that the proof by mathematical induction and the proof by strong induction are equivalent
Prove that the proof by mathematical induction and the proof by strong induction are equivalent
Use the laws of propositional logic to prove that the followingcompound propositions are logically equivalent....
Use the laws of propositional logic to prove that the following compound propositions are logically equivalent.A. ? ↔ (? ∧ ?) and ? → ?B. ¬(? ∨ (? ∧ (? → ?))) and ¬? ∧ (? → ?)
Determine whether the statements in (a) and (b) are logically equivalent. Bob is both a math...
Determine whether the statements in (a) and (b) are logically equivalent. Bob is both a math and computer science major and Ann is a math major, but Ann is not both a math and computer science major. It is not the case that both Bob and Ann are both math and computer science majors, but it is the case that Ann is a math major and Bob is both a math and computer science major.
Prove the following: theorem: every topological group is completely regular. Proof. Let V0 be a neighborhood...
Prove the following: theorem: every topological group is completely regular. Proof. Let V0 be a neighborhood of the identity elemetn e, in the topological group G. In general, coose Vn to be a neighborhood of e such that Vn.VncVn-1. Consider the set of all dyadic rationals p, that is all ratinal number of the form k/sn, with k and n inegers. FOr each dyadic rational p in (0,1], define an open set U(p) inductively as foloows: U(1)=V0 and
Two compound propositions p and q in propositional logic are logically equivalent if . . ..
Complete the following statements.Two compound propositions p and q in propositional logic are logically equivalent if . . ..An argument form in propositional logic is valid if . . ..A theorem is a statement that . . ..A statement that is assumed to be true is called a(n) . . ..A proof is a valid argument that . . ..
49. Which of the following is the most logically sound proof in favour of God’s existence?...
49. Which of the following is the most logically sound proof in favour of God’s existence? (A) \Every society throughout human history has had some notion of God, and there-fore God must exist." (B) \I feel God’s existence through the Holy Spirit, and therefore know that He exists." (C) \Everything that begins to exist has a cause. The universe began to exist. There-fore, the universe has a cause, which I call God." (D) \It is ridiculously unlikely that the universe...
Do the following proofs deductively. Justify each step in your proof with a law or inference...
Do the following proofs deductively. Justify each step in your proof with a law or inference rule. a) If P ⇒ Q, ¬R ⇒¬Q, and P then prove R. b) If P ⇒ (Q ∧ R) and ¬R ∧ Q then prove ¬P.
Prove the following using the method suggested: (a) Prove the following either by direct proof or...
Prove the following using the method suggested: (a) Prove the following either by direct proof or by contraposition: Let a ∈ Z, if a ≡ 3 (mod 5) and b ≡ 2 (mod 5), then ab ≡ 1 (mod 5). (b) Prove the following by contradiction: Suppose a, b ∈ Z. If a² + b² is odd, then (2|a) ⊕ (2|b), where ⊕ is the exclusive disjuntion, i.e. p ⊕ q = (p ∨ q) ∧ ¬(p ∧ q). (d)...
Prove that the following statements are equivalent. A. The Euclidean parallel postulate holds. B. Given any...
Prove that the following statements are equivalent. A. The Euclidean parallel postulate holds. B. Given any triangle △ABC and given any segment DE, there exists a triangle △DEF having DE as one of its sides such that △ABC ∼ △DEF (Wallis’ postulate on the existance of similar triangles). (you cannot use measures)
prove the following statement: If the augmented matrices of two linear systems are row equivalent, then...
prove the following statement: If the augmented matrices of two linear systems are row equivalent, then those systems are equivalent. (To do this, start with a solution to one of the systems and show that it is still a solution of the other system under each of the three elementary row operations.)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT