BBC News Reality Check

Asked about her plans to tackle the cost of living crisis, Liz Truss said: "What I would do immediately is reverse the National Insurance increase, keeping more money in people's pockets, also have a temporary moratorium on the green energy levy to cut fuel bills."

National Insurance (NI) increased by 1.25p in the pound in April.

Reversing that would make no difference for anybody earning less than £12,570 a year because they don’t pay NI.

For someone earning £20,000 a year they would save £93 a year. Someone earning £30,000 would save £218.

The green levy is an amount the government makes energy companies add to bills to pay for things like schemes to help fund renewable energy and provide grants for insulation. Removing it would knock about £153 off an average annual dual fuel bill, according to the regulator Ofgem.

Analysts Cornwall Insight have warned that energy bills for a typical household could hit £4,266 a year, in January, up from £1,971 at the moment.

You can read more about the tax policies of the Tory leadership candidates here

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In Trump's statement about Monday's FBI search, he reacted angrily and compared his situation to that of his former Democratic rival Hillary Clinton.

“Hillary Clinton was allowed to delete… 33,000 emails after they were subpoenaed by Congress. Absolutely nothing has happened to hold her accountable," he claimed.

This claim refers to an investigation into Clinton’s use of a private email server for government business, which is against official protocol. In March 2015, after she’d left office as secretary of state, the company that maintained her email server deleted the archive mailbox, erasing about 32,000 emails, including some from when she was in her official role.

This happened after Congress had already asked Clinton to hand over any work-related emails. She did hand over thousands of other emails, and said she believed the deleted emails were not work-related.

The FBI later investigated and found she was “extremely careless” with government material.

But it said there was no evidence of collusion between her and the company that maintained the server to improperly delete work-related emails, or that Clinton was “allowed” to delete these emails as Trump suggests.

There have been some more cyber-attacks reported against official websites in Taiwan.

The Ministry of National Defence was one target, as well as the Environment Protection Bureau in Kaohsiung, a city in southern Taiwan, according to local media. The Defence Ministry's website went offline temporarily and on the environment bureau's website, the cyber-attackers put up five Chinese national flags.

The website of Taiwan's presidential office, the Foreign Ministry and the governing party have all been targeted this week.

Taiwan says the identities of those responsible for the latest attacks remains unknown.

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Misleading information has been circulating in recent days as tensions have surged.

Reports emerged incorrectly claiming that the international airport near Taiwan’s capital, Taipei, was hit by a missile on 2 August.

But Taiwan’s Ministry of National Defence denied this had happened, and pointed out the airport was working normally.

There've also been claims in some Chinese-language media that Taiwan has cancelled all leave for its military. But as yet this has not happened, although personnel have been asked to remain "on alert."

There's also been misleading video shared claiming to show Chinese warships in the waters around Taiwan in recent days. But it uses old footage of events held to mark the 73rd anniversary of the Chinese navy in April.

Similarly, social media users have shared video said to show a recent Chinese military exercise, which was actually a Taiwanese drill from nearly two years ago.

Beijing has repeatedly called on Washington to honour a deal to reduce US arms sales to Taiwan, and says these promises have been broken.

In 1982, President Ronald Reagan agreed to a gradual reduction in military sales, but added a condition that this would depend on "the commitment of China to a peaceful solution" with Taiwan, which China considers to be a breakaway province.

No agreement was reached on the timescale for this reduction or the form it would take.

Over the decades, the value of US arms sales to Taiwan has fluctuated widely.

The single biggest purchase was made in 1992 by former Taiwan President Lee Teng-hui, following a policy to enhance Taiwan’s independent defence capabilities.

In 2007 Taiwan significantly increased its defence budget, leading to a significant increase in arms purchased from the US.

Former US President Barack Obama (in office between 2009-2017) approved three separate arms deals, with a total value of $12bn over eight years.

His successor Donald Trump signed deals worth at least $14bn during his four years in office.

President Joe Biden has so far signed deals worth just over $1bn.

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