- Mar 2024
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math.libretexts.org math.libretexts.org
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∀x)(M(x)∧U(x)→B(x)
every mathemathical book published in the USA has a blue cover
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∃x)(¬B(x
there is at least one book which has no blue cover
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(∃x)(A(x)∧(¬M(x))).(∃x)(A(x)∧(¬M(x))).(\exists x)(A(x) \land (\neg M(x)))\text{.}
There is an animal which is not warm-blooded
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Translate into English: (∀x)(F(x)→S(x)).
every fish lives in the sea
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Translate into English: (∃x)(S(x)∧¬F(
there is at least one thing that lives in the sea and is not a fish
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math.libretexts.org math.libretexts.org
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∃x∈R(x2<0)∃x∈R(x2<0)\exists x\in\mathbb{R} \, (x^2 < 0).
there is at least a real number whose square is negative!
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For all integers kkk, the integer 2k2k2k is even
true
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There exists an integer kkk such that 2k+12k+12k+1 is even.
this is not true
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Name a few more examples of twin primes.
17 and 19
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ere exists a prime number xxx such that x+2x+2x+2 is also prim
such as 3?
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∃x∈R(x>5)
This tells us that there is at least one real number which is more than 5. This is true just with one number such as 5.1. But there are many more which makes this true, we don´t need them, yet it is good to know it
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∃x
There is at least one thing which makes true whatever tells us what is written at the right side of thi
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∀x∈S
it is something obvious but I like to remark it. The left part set a measure for how many things this is true. This is why the name is quantifier. Meanwhile the right part means something either true or false. It is necesary to quantify it, because the setnence could be true for a certain number of things
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(x is a Discrete Mathematics student⇒x has taken Calculus I and Calculus II)
The right stuff means something that could be true or false |
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