FRUITS AND VEGETABLES in Israel
Unlike in other parts of the world, in Israel fruits and vegetables are NOT automatically "kosher" - here we need to make sure that they are not "orlah" fruits (harvested during a tree's first 3 yrs, with other rules applying to year 4) and that trumot and ma'asrot have been taken (from both fruits and vegetables).
If you shop at a market that doesn't have an ishur kashrut (kosher certification) on their produce, you'll need to investigate these issues further, if you are interested in adhering to the halachot of the Land of Israel OR if you regularly host people who assume the food in your home is kosher! I must say that it's important to familarize yourself with these special halachot, as they are part of keeping kosher in Israel! (If you say you keep Kosher in Israel, everyone assumes that you have taken care of these issues; and if you don't, then you may be unwittingly putting someone in a situation they don't want to be in!)
It's definitely possible to take trumot and maasrot on your own (I do it often), so vegetables are easiest to buy without a teudah, as that is all you need to do (and very often, it would be without a bracha). Some of the fruits on the market may be ok to purchase even from a non-certified establishment and just take trumot and maasrot, because of the extremely low percentage of orlah fruits being sold, but those lists change frequently, so you'll constantly need to stay up-to-date.
Other fruits can be a problem, because of a high possibility that they are orlah (from the first 3 yrs after the tree was planted). I have recently begun to post a monthly update on my website, with a list of the fruits where the percentage of orlah fruits on the open market is greater than 0.5%, so should only be bought from a reputable source that does not sell orlah fruits (i.e. a place with a teudah):
Update for Av 5777
Fruits to AVOID buying without a teudah:
Prickly Pear (Sabra Fruit)
Seedless Grapes (Round Green)
Please be sure to speak with your personal Halachic Authority about purchasing fruit in Israel without a teudah. Not everyone holds by the 0.5% threshold. This information is just for informational purposes and is not a halachic psak! Even if you follow a psak that relies on the 0.5% threshold, you still must take trumot and maasrot on all produce grown in Israel (or be sure it has been taken), in order to fulfill your halachic obligations.
Also, this list does not apply to fruit grown by an individual. If your friend has a fruit tree, you'll need to find out how old it is!
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