Q: If a set of sets is infinite or contains an infinite element, then its union is infinite. The powerset of an infinite set is infinite. Any superset of an infinite set is infinite. If an infinite set is partitioned into finitely many subsets, then at least one of them must be infinite. Any set which can be mapped onto an infinite set is infinite. The Cartesian product of an infinite set and a nonempty set is infinite. The Cartesian product of an infinite number of sets each containing at least two elements is either empty or infinite; if the axiom of choice holds, then it is infinite.
Can we conclude that is the union of two infinite sets always an infinite set?
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A: yes
Five of St Aubyn's novels, Never Mind, Bad News, Some Hope, Mother's Milk, and At Last, form The Patrick Melrose Novels, the first four of which were republished in a single volume in 2012, in anticipation of the fifth. They are based on the author's own life, growing up in a highly dysfunctional upper-class English family, dealing with the deaths of both parents, alcoholism, heroin addiction and recovery, and marriage and parenthood.
is the show patrick melrose based on a true story?
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Answer: yes
The minimum amount is Rs.500 which can be deposited. The rate of interest at present is 7.6% per annum, which is also tax-free. The entire balance can be withdrawn on maturity. Interest received is tax free. The maximum amount which can be deposited every year is Rs. 1,50,000 in an account at present. The interest earned on the PPF subscription is compounded annually. All the balance that accumulates over time is exempted from wealth tax. Moreover, it has low risk -- risk attached is Government risk. PPF is available at post offices and banks.

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do we need to pay tax on ppf interest?

A: no
Problem: Text: There is no legal statute specifically prohibiting the carry of a firearm other than a handgun (pre-1899 black powder weapons, and replicas of such, are not legally firearms in Texas). However, if the firearm is displayed in a manner ''calculated to cause alarm,'' then it is ''disorderly conduct''. Open carry of a handgun in public had long been illegal in Texas, except when the carrier was on property he/she owned or had lawful control over, was legally hunting, or was participating in some gun-related public event such as a gun show. However, the 2015 Texas Legislature passed a bill to allow concealed handgun permit holders to begin carrying handguns openly. The bill was signed into law on June 13, 2015, and took effect on January 1, 2016. A License to Carry (LTC) is still required to carry a handgun openly or concealed in public.

Question: can i carry a gun in texas without a license?

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A: no
IN: Is it true that is mild steel the same as carbon steel?

Mild steel (iron containing a small percentage of carbon, strong and tough but not readily tempered), also known as plain-carbon steel and low-carbon steel, is now the most common form of steel because its price is relatively low while it provides material properties that are acceptable for many applications. Mild steel contains approximately 0.05--0.25% carbon making it malleable and ductile. Mild steel has a relatively low tensile strength, but it is cheap and easy to form; surface hardness can be increased through carburizing.

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OUT: no
IN: Is it true that can male and female dwarf gouramis live together?

Once the nest has been built the male will begin courting the female, usually in the afternoon or evening. He signals his intentions by swimming around the female with flared fins, attempting to draw her to the nest where he will continue his courting display. If the female accepts the male she will begin swimming in circles with the male beneath the bubble nest. When she is ready to spawn she touches the male on either the back or the tail with her mouth. Upon this signal the male will embrace the female, turning her first on her side and finally on her back. At this point the female will release approximately five dozen clear eggs, which are immediately fertilized by the male. Most of the eggs will float up into the bubble nest. Eggs that stray are collected by the male and placed in the nest. Once all the eggs are secured in the nest, the pair will spawn again. If more than one female is present in the breeding tank, the male may spawn with all of them. The spawning sessions will continue for two to four hours, and produce between 300 and 800 eggs. Dwarf gouramis have a fecundity of about 600 eggs.(1) Upon completion, the male will place a fine layer of bubbles beneath the eggs, assuring that they remain in the bubble nest.The male will protect the eggs and fry. In 12 to 24 hours the fry will hatch, and continue developing within the protection of the bubble nest. After three days they are sufficiently developed to be free swimming and leave the nest. When the fry are two to three days old the male should also be removed or he may consume the young.

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OUT:
yes