You can look up the tx of a btc address in the browser by using a blockchain explorer:
https://blockchain.infoIf the tx is not listed there, it was not send!
You can also do the following in Electrum:
1) Go to the Address tab,
2) Right click on the address you gave the other person, the one to be used for the transaction,
3) Click on 'View on block explorer' on the menu that pops up,
That will open the block explorer you have set in the preferences of Electrum and will show you that specific address together with all transactions linked to that address.