with the next step being Mountain Lion, 10.8.x which could be had for the princely sum of $19.99
The updates to ML contain a new version of Safari.
However, this is no longer available in the App store but may be via Amazon or eBay.
That said, we do not know the version of MBA that you are using but all of the MBA's from Mid 2009 onwards can support the latest version of OS X , 10.11.x with the earlier ones not giving a particularly good user experience.
The initial release of the MBA, January 2008, only supports up to OS X 10.7.5
P
I have a MacBook Air OS 10.7.5 (Lion) and I have gotten a few pop-up messages that Firefox will require a later OS. Does that mean I will have to try and upgrade my OS? Will another browser work? Safire does not play well with my Mac which is why I went to Firefox. I definitely want to avoid messing around with my OS. Thank you,

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