BBC News Reality Check

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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Right at the end of the debate, when asked whether Brexit was to blame for travel chaos at Dover, both candidates answered "No".

But Brexit is one of the factors involved.

When the UK was in the EU, there was much less need for rigorous checks there for those entering France because UK citizens could travel freely around the EU.

This ended with Brexit and now French officials at Dover have to stamp and check passports.

This can take up to a minute per person - according to travel expert Simon Calder - rather than a few seconds (under the old system). Other factors that have contributed to the disruption include an initial shortage in French border staff at Dover on Friday.

Read more here.

As we predicted earlier in the evening, Liz Truss defended her Brexit credentials, saying: "Since the referendum took place I've delivered dozens of trade deals."

The UK has secured trade agreements with more than 60 countries since the Brexit vote and Ms Truss served as International Trade Secretary from 2019-2021.

However, the vast majority are "rollover" deals - copying the terms of deals the UK already had when it was an EU member, rather than creating new benefits.

The UK has negotiated two new deals from scratch – with Australia and New Zealand. The government’s own estimate says the Australia deal could increase the UK's GDP by just 0.08% over 15 years.

More on this here.

When asked how he would help households with the rising cost of living, Rishi Sunak focused on cutting energy bills by helping millions of homes with installing insulation.

However, over the last decade installation rates have fallen by 98%.

When Rishi Sunak was chancellor, the government scrapped the green homes grant scheme which was offering £10,000 to homes to help install insulation, after achieving just 10% of its target.

And two weeks later the Telegraph reported that the Treasury blocked proposals by Business Secretary Kwasi Kwarteng to expand the Energy Company Obligation – an energy efficiency scheme to help low income households.

Talking about the possibility of government borrowing rising under her policies, Liz Truss said: "Countries like the US, Canada, and Japan, all have higher levels of debt than the UK, but they are not following the policies that will lead to a recession. We are an outlier."

She has previously specified that she is talking about debt per person when making that comparison.

At the end of 2021, UK government debt stood at £2.4 trillion. That translates to roughly £38,000 per person in the UK. Of the G7 countries, the UK's government debt is the second lowest behind Germany at roughly £30,000 per person. Japan has the highest government debt per person at £86,000, for the United States it's £71,000 and for Canada £49,000. Since 2010, government debt per person in the UK has increased from around £24,000 to £38,000 in 2021.