Donald Trump and Kamala Harris went head to head in their first televised debate in the US election campaign.

In 90 minutes of often fiery exchanges, the Republican and Democratic presidential candidates traded claims over key election issues including the economy, immigration and abortion.

BBC Verify has been examining them.

CLAIM: Trump: “In Springfield, they’re [immigrants] eating the dogs, the people that came in, they’re eating the cats, they’re eating the pets of people that live there”.

VERDICT: There is no evidence that this is happening.

Trump’s comment followed a baseless claim – which was shared by his vice-presidential candidate JD Vance – that immigrants from Haiti who have recently settled in Springfield, Ohio, have been eating pets.

Springfield city officials told BBC Verify: “There have been no credible reports or specific claims of pets being harmed, injured or abused by individuals within the immigrant community.”

You can read more here.

CLAIM: Harris: “Donald Trump left us the worst unemployment since the Great Depression”.

VERDICT: This is false.

At the end of Trump’s term of office in January 2021, the unemployment rate was 6.4%.

But it has been higher since the Great Depression.

In October 2009, unemployment peaked at 10% in a period of deep economic recession.

It has fallen steadily since, apart from a sharp peak during the Covid pandemic, and in the most recent data for August 2024, unemployment stood at 4.2%.

CLAIM: Trump: “We have millions of people pouring into our country from prisons and jails, from mental institutions and insane asylums”.

VERDICT: There is no evidence for these kind of numbers.

There have been about 10 million encounters with migrants crossing over the US border since January 2021.

There are no publicly available figures on how many of them have served time in prison or come from mental institutions but there is some data on how many have previous criminal convictions.

Of the 1.4 million apprehensions of people crossing the border illegally so far this financial year (to September 2024) – and where the Border Patrol was able to check against law enforcement databases – about 14,700 people had previous criminal convictions.

That’s equivalent to roughly 1% of all border apprehensions in this period and doesn’t amount to the “millions” Trump is claiming.

CLAIM: Harris: “If Donald Trump were to be re-elected, he will sign a national abortion ban”.

VERDICT: This is misleading. Trump has denied that he would sign a national ban if elected president.

He has said that he would leave limits on abortion access up to individual states to decide.

Here, Harris also talked about “his Project 2025” – a reference to a document published by the right-wing Heritage Foundation outlining a list of policy proposals that they believe a Trump presidency should implement.

It doesn’t propose a national ban either, but it does recommend limiting abortion access.

Trump has distanced himself from the document, saying: “I know nothing about Project 2025. I have no idea who is behind it.”

Many former Trump administration officials are associated with Project 2025.

CLAIM: Trump: “The worst inflation we’ve ever had” [was under Biden].

VERDICT: This is false.

Under President Biden, inflation peaked at 9.1% in June 2022, at a time when prices were rising sharply in many countries.

Inflation was last above 9% in 1981, but it has been significantly higher than that at several other points in US history.

Since its peak in mid-2022, inflation has dropped to 2.9%, for the year to July 2024. But prices are still rising and it is a key issue for many voters.

CLAIM: Harris: “Economists have said that that Trump sales tax would actually result for middle class families in about $4,000 more a year”.

VERDICT: Harris calls Trump’s proposed tax on imports a sales tax. Some economists have estimated that these tariffs could cost families this much. Others have lower estimates.

Trump insists the cost would be felt by foreign countries but economists believe there would be an economic cost for US importers and consumers.

The $4,000 figure comes from analysis – by the left-of-centre think tank the Centre for American Progress – of Trump’s pledge to increase tariffs on all imported goods to 10-20% and all goods imported from China to 60%.

They took the amount the US buys in goods from abroad annually, figured out how much the new taxes on these goods would be and divided this by the number of households in the US.

It works out at $4,600 per household, but when you look at “middle income” families you get a figure of $3,900 a year.

Other estimates are lower. The Peterson Institute thinks the impact would be closer to $1,700 a year (for tariffs at 10%) or $2,500 (at 20%).

CLAIM: Trump: “Crime in Venezuela… is way down because they have taken their criminals off the streets and given them to her [Harris] to put into our country”.

VERDICT: There is no evidence that Venezuela is doing this. Crime levels are down but experts say this is because of the state of the economy.

The Venezuelan government does not publish reliable crime figures, but the independent Venezuelan Observatory of Violence does.

The Observatory’s 2023 annual report said that violent deaths that year – such as homicides – were down by a quarter compared to 2022.

The Observatory told BBC Verify: “Crime is reduced in Venezuela by a reduction in crime opportunities: bank robberies disappear because there is no money to steal; kidnappings are reduced because there is no cash to pay ransoms.”

It said it had seen no evidence that the Venezuelan government was sending criminals to the US.

Reporting by Lucy Gilder, Merlyn Thomas, Daniele Palumbo, Gerry Georgieva & Kayleen Devlin.

North America correspondent Anthony Zurcher makes sense of the race for the White House in his weekly US Election Unspun newsletter.

Readers in the UK can sign up here. Those outside the UK can sign up here.