Issue Excluding Entries with Multiple Categories in Query
Start by getting the category ID(s) you want to exclude:



{% set categoryIds = craft.categories()
    .group('categories')
    .slug('category-one')
    .ids() %}


Then get all the entry IDs that are related to them, which should be excluded:

{% set excludeIds = craft.entries()
    .relatedTo({
        targetElement: categoryIds
    })
    .ids() %}


Then run your main news query, excluding those entry IDs.

{% set latestNews = craft.entries()
    .section('news')
    .id(['not']|merge(excludeIds))
    .with([
        ['image', {
            withTransforms: ['medium']
        }]
    ])
    .orderBy('postDate desc')
    .limit(4)
    .all() %}