グローバルビジネスで役立つ数学（70）必要条件と十分条件（英語版）

Hi there!

The fly in the ointment is the fact that many businesspeople attend a business seminar or sign up for a business school to apparently enhance their negotiation and presentation skills.

How much money do they spend just listening to their plausible talks in Japanese? Hundreds of thousands of yen for only two to three weeks of seminar or workshop? Come on! Don’t you realize it’s nothing but a rip-off? Don’t settle for the second or third best as one of the information have-nots.

My Business English Class costs less than 200,000 yen covering 40 lessons, 80 minutes per class, a year.

You’ll be surprised at the content given in my class; 1) small talk (speaking), 2) written tests online (listening, reading & writing), 3) summarization (listening, writing & speaking), 4) discussion, debate, interpretation, or presentation (speaking), and 5) wrap-up of the day.

Remember. In my Business English Class, you can not only study Business English but also acquire a sense of business by sharing your opinions with classmates. You might want to invest your precious money NOT in passive role-play games BUT in actively participating in discussion and debate.

An old saying tells us, “Too much knowledge inhibits creativity.” I would say the key to business success is being assertive and thinking outside the box. You’ll never be a winner as long as you stay in the audience of such lectures.

I’ve never read any business books because I try not to be biased by stereotype success stories; however, my consultancy success ratio occupies over 80%. My clients’ turnover has almost increased compared to the previous fiscal year by a synergy effect with me.

What matters most is not to attend but participate. If you’re interested in my Business English Class, feel free to contact me at Experts-At-Practical English. I am happy to let you have a knack for improving your English communication skills.

Today, I challenge a word problem related to necessary and sufficient mathematical conditions, where you may find requirements for being a successful businessperson.

Match each of the following 1) necessary, 2) sufficient, and 3) necessary and sufficient conditions with the one that satisfies the formula \(x^{2} = 9\) for the real number \(x\) respectively for ① \(x = 3\) ② \(x = -3\) or \(x = 3\) ③ \(|x| > 0\). (Source: Yellow Chart Math Ⅰ＋Ａ similar question made from P70)

Here is my solution to the problem.

Regarding ①、
\(x = 3\Longrightarrow x^{2} = 9\) is true.
However, \(x^{2} = 9\Longrightarrow x = 3\) is false because we have \(x = -3\) as a counter-example.

Regarding ②,
\(x = -3\) or \(x = 3\Longrightarrow x^{2} = 9\) is true.
Also, \(x^{2} = 9\longrightarrow x = -3 or x = 3\) is true.

Regarding ③,
\(|x| > 0\Longrightarrow x^{2} = 9\) is false because we have \(x = 1\) as a counter-example.
Then, \(x^{2} = 9\Longrightarrow|x| > 0\) is true.

Therefore, the correct answer is (1)-③, (2)-①, and (3)-②.

Once again, special thanks to Yellow Chart Math Ⅰ＋Ａ.

Winners never quit. Quitters never win; so does business consultancy go.

Stay tuned, and expect to see my next post.

Keep well.

Frank Yoshida

￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣
【グローバルビジネスで役立つ数学】でもっと学習する b＾＾)
【参考図書】『もう一度高校数学』（著者：高橋一雄氏）株式会社日本実業出版社
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